derived_lemma(inc(euler(c,[a,b]),side_bis([c,orthocenter([a,b],c)])),['GL01','L52','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([c,foot(b,[a,c])])),['GL01','L53','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([c,foot(a,[b,c])])),['GL01','L54','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([b,orthocenter([a,b],c)])),['GL01','L49','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([b,foot(a,[b,c])])),['GL01','L50','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([b,foot(c,[a,b])])),['GL01','L51','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([a,orthocenter([a,b],c)])),['GL01','L46','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([a,foot(b,[a,c])])),['GL01','L47','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([a,foot(c,[a,b])])),['GL01','L48','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([c,a])),['GL01','L43','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([c,foot(a,[b,c])])),['GL01','L44','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([c,foot(c,[a,b])])),['GL01','L45','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([a,foot(b,[a,c])])),['GL01','L41','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([a,foot(a,[b,c])])),['GL01','L42','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([b,foot(b,[a,c])])),['GL01','L38','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([b,foot(c,[a,b])])),['GL01','L39','GD02']).
derived_lemma(inc(point_n(c,[a,b]),side_bis([b,a])),['GL01','L35','GD02']).
derived_lemma(inc(point_n(c,[a,b]),side_bis([b,incenter([a,b],c)])),['GL01','L36','GD02']).
derived_lemma(inc(point_n(b,[a,c]),side_bis([a,incenter([a,b],c)])),['GL01','L34','GD02']).
derived_lemma(inc(point_n(a,[b,c]),side_bis([c,b])),['GL01','L31','GD02']).
derived_lemma(inc(point_n(a,[b,c]),side_bis([c,incenter([a,b],c)])),['GL01','L32','GD02']).
derived_lemma(inc(angle_bis_foot(c,[a,b]),side_bis([foot(angle_bis_foot(c,[a,b]),line([a,c])),foot(angle_bis_foot(c,[a,b]),line([b,c]))])),['GL01','L30','GD02']).
derived_lemma(inc(angle_bis_foot(b,[a,c]),side_bis([foot(angle_bis_foot(b,[a,c]),line([a,b])),foot(angle_bis_foot(b,[a,c]),line([b,c]))])),['GL01','L29','GD02']).
derived_lemma(inc(angle_bis_foot(a,[b,c]),side_bis([foot(angle_bis_foot(a,[b,c]),line([a,b])),foot(angle_bis_foot(a,[b,c]),line([a,c]))])),['GL01','L28','GD02']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,a_k])),['GL01','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,b_k])),['GL01','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,c_k])),['GL01','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n(a,[b,c])])),['GL01','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n(b,[a,c])])),['GL01','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n(c,[a,b])])),['GL01','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n_k(a,[b,c])])),['GL01','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n_k(b,[a,c])])),['GL01','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,point_n_k(c,[a,b])])),['GL01','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,a])),['GL01','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c,b])),['GL01','L12','D26']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[b,c]),foot_ima(a)])),['GL01','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[b,c]),foot_ima(b)])),['GL01','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[b,c]),foot_ima(c)])),['GL01','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[b,c]),foot(incenter([a,b],c),[a,c])])),['GL01','L13','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[b,c]),foot(incenter([a,b],c),[a,b])])),['GL01','L14','D27']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),midpoint([a,c])])),['GL01','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),midpoint([a,b])])),['GL01','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),foot(a,[b,c])])),['GL01','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),foot(b,[a,c])])),['GL01','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),foot(c,[a,b])])),['GL01','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),euler(a,[b,c])])),['GL01','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),euler(b,[a,c])])),['GL01','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([b,c]),euler(c,[a,b])])),['GL01','L24','D32']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,c])),['GL01','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,b_k])),['GL01','D38','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,c_k])),['GL01','D38','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n(a,[b,c])])),['GL01','D38','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n(b,[a,c])])),['GL01','D38','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n(c,[a,b])])),['GL01','D38','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n_k(a,[b,c])])),['GL01','D38','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n_k(b,[a,c])])),['GL01','D38','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,point_n_k(c,[a,b])])),['GL01','D38','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,a])),['GL01','D38','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a_k,b])),['GL01','D38','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,c])),['GL01','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,a_k])),['GL01','D39','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,c_k])),['GL01','D39','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n(a,[b,c])])),['GL01','D39','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n(b,[a,c])])),['GL01','D39','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n(c,[a,b])])),['GL01','D39','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n_k(a,[b,c])])),['GL01','D39','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n_k(b,[a,c])])),['GL01','D39','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,point_n_k(c,[a,b])])),['GL01','D39','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,a])),['GL01','D39','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b_k,b])),['GL01','D39','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,c])),['GL01','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,a_k])),['GL01','D40','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,b_k])),['GL01','D40','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n(a,[b,c])])),['GL01','D40','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n(b,[a,c])])),['GL01','D40','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n(c,[a,b])])),['GL01','D40','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n_k(a,[b,c])])),['GL01','D40','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n_k(b,[a,c])])),['GL01','D40','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,point_n_k(c,[a,b])])),['GL01','D40','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,a])),['GL01','D40','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([c_k,b])),['GL01','D40','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),c])),['GL01','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),a_k])),['GL01','D47','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),b_k])),['GL01','D47','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),c_k])),['GL01','D47','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),point_n(b,[a,c])])),['GL01','D47','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),point_n(c,[a,b])])),['GL01','D47','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),point_n_k(a,[b,c])])),['GL01','D47','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),point_n_k(b,[a,c])])),['GL01','D47','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),point_n_k(c,[a,b])])),['GL01','D47','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),a])),['GL01','D47','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(a,[b,c]),b])),['GL01','D47','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),c])),['GL01','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),a_k])),['GL01','D48','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),b_k])),['GL01','D48','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),c_k])),['GL01','D48','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),point_n(a,[b,c])])),['GL01','D48','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),point_n(c,[a,b])])),['GL01','D48','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),point_n_k(a,[b,c])])),['GL01','D48','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),point_n_k(b,[a,c])])),['GL01','D48','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),point_n_k(c,[a,b])])),['GL01','D48','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),a])),['GL01','D48','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(b,[a,c]),b])),['GL01','D48','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),c])),['GL01','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),a_k])),['GL01','D49','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),b_k])),['GL01','D49','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),c_k])),['GL01','D49','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),point_n(a,[b,c])])),['GL01','D49','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),point_n(b,[a,c])])),['GL01','D49','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),point_n_k(a,[b,c])])),['GL01','D49','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),point_n_k(b,[a,c])])),['GL01','D49','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),point_n_k(c,[a,b])])),['GL01','D49','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),a])),['GL01','D49','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n(c,[a,b]),b])),['GL01','D49','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),c])),['GL01','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),a_k])),['GL01','D50','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),b_k])),['GL01','D50','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),c_k])),['GL01','D50','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),point_n(a,[b,c])])),['GL01','D50','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),point_n(b,[a,c])])),['GL01','D50','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),point_n(c,[a,b])])),['GL01','D50','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),point_n_k(b,[a,c])])),['GL01','D50','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),point_n_k(c,[a,b])])),['GL01','D50','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),a])),['GL01','D50','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(a,[b,c]),b])),['GL01','D50','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),c])),['GL01','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),a_k])),['GL01','D51','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),b_k])),['GL01','D51','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),c_k])),['GL01','D51','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),point_n(a,[b,c])])),['GL01','D51','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),point_n(b,[a,c])])),['GL01','D51','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),point_n(c,[a,b])])),['GL01','D51','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),point_n_k(a,[b,c])])),['GL01','D51','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),point_n_k(c,[a,b])])),['GL01','D51','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),a])),['GL01','D51','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(b,[a,c]),b])),['GL01','D51','L12','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),c])),['GL01','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),a_k])),['GL01','D52','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),b_k])),['GL01','D52','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),c_k])),['GL01','D52','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),point_n(a,[b,c])])),['GL01','D52','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),point_n(b,[a,c])])),['GL01','D52','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),point_n(c,[a,b])])),['GL01','D52','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),point_n_k(a,[b,c])])),['GL01','D52','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),point_n_k(b,[a,c])])),['GL01','D52','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),a])),['GL01','D52','L11','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([point_n_k(c,[a,b]),b])),['GL01','D52','L12','D26']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(a),foot(incenter([a,b],c),[b,c])])),['GL01','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(a),foot_ima(b)])),['GL01','D65','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(a),foot_ima(c)])),['GL01','D65','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(a),foot(incenter([a,b],c),[a,c])])),['GL01','D65','L13','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(a),foot(incenter([a,b],c),[a,b])])),['GL01','D65','L14','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(b),foot(incenter([a,b],c),[b,c])])),['GL01','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(b),foot_ima(a)])),['GL01','D66','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(b),foot_ima(c)])),['GL01','D66','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(b),foot(incenter([a,b],c),[a,c])])),['GL01','D66','L13','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(b),foot(incenter([a,b],c),[a,b])])),['GL01','D66','L14','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(c),foot(incenter([a,b],c),[b,c])])),['GL01','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(c),foot_ima(a)])),['GL01','D67','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(c),foot_ima(b)])),['GL01','D67','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(c),foot(incenter([a,b],c),[a,c])])),['GL01','D67','L13','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot_ima(c),foot(incenter([a,b],c),[a,b])])),['GL01','D67','L14','D27']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,a_k])),['GL01','L11','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,b_k])),['GL01','L11','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,c_k])),['GL01','L11','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n(a,[b,c])])),['GL01','L11','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n(b,[a,c])])),['GL01','L11','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n(c,[a,b])])),['GL01','L11','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n_k(a,[b,c])])),['GL01','L11','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n_k(b,[a,c])])),['GL01','L11','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([a,point_n_k(c,[a,b])])),['GL01','L11','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,a_k])),['GL01','L12','D38','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,b_k])),['GL01','L12','D39','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,c_k])),['GL01','L12','D40','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n(a,[b,c])])),['GL01','L12','D47','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n(b,[a,c])])),['GL01','L12','D48','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n(c,[a,b])])),['GL01','L12','D49','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n_k(a,[b,c])])),['GL01','L12','D50','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n_k(b,[a,c])])),['GL01','L12','D51','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,point_n_k(c,[a,b])])),['GL01','L12','D52','D26']).
derived_lemma(inc(circumcenter([a,b],c),side_bis([b,a])),['GL01','L12','L11','D26']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,c]),foot(incenter([a,b],c),[b,c])])),['GL01','L13','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,c]),foot_ima(a)])),['GL01','L13','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,c]),foot_ima(b)])),['GL01','L13','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,c]),foot_ima(c)])),['GL01','L13','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,c]),foot(incenter([a,b],c),[a,b])])),['GL01','L13','L14','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,b]),foot(incenter([a,b],c),[b,c])])),['GL01','L14','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,b]),foot_ima(a)])),['GL01','L14','D65','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,b]),foot_ima(b)])),['GL01','L14','D66','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,b]),foot_ima(c)])),['GL01','L14','D67','D27']).
derived_lemma(inc(incenter([a,b],c),side_bis([foot(incenter([a,b],c),[a,b]),foot(incenter([a,b],c),[a,c])])),['GL01','L14','L13','D27']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),midpoint([b,c])])),['GL01','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),midpoint([a,b])])),['GL01','L17','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),foot(a,[b,c])])),['GL01','L17','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),foot(b,[a,c])])),['GL01','L17','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),foot(c,[a,b])])),['GL01','L17','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),euler(a,[b,c])])),['GL01','L17','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),euler(b,[a,c])])),['GL01','L17','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,c]),euler(c,[a,b])])),['GL01','L17','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),midpoint([b,c])])),['GL01','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),midpoint([a,c])])),['GL01','L18','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),foot(a,[b,c])])),['GL01','L18','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),foot(b,[a,c])])),['GL01','L18','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),foot(c,[a,b])])),['GL01','L18','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),euler(a,[b,c])])),['GL01','L18','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),euler(b,[a,c])])),['GL01','L18','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([midpoint([a,b]),euler(c,[a,b])])),['GL01','L18','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),midpoint([b,c])])),['GL01','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),midpoint([a,c])])),['GL01','L19','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),midpoint([a,b])])),['GL01','L19','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])])),['GL01','L19','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])])),['GL01','L19','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),euler(a,[b,c])])),['GL01','L19','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),euler(b,[a,c])])),['GL01','L19','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(a,[b,c]),euler(c,[a,b])])),['GL01','L19','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),midpoint([b,c])])),['GL01','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),midpoint([a,c])])),['GL01','L20','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),midpoint([a,b])])),['GL01','L20','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])])),['GL01','L20','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])])),['GL01','L20','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),euler(a,[b,c])])),['GL01','L20','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),euler(b,[a,c])])),['GL01','L20','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(b,[a,c]),euler(c,[a,b])])),['GL01','L20','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),midpoint([b,c])])),['GL01','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),midpoint([a,c])])),['GL01','L21','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),midpoint([a,b])])),['GL01','L21','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])])),['GL01','L21','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])])),['GL01','L21','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),euler(a,[b,c])])),['GL01','L21','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),euler(b,[a,c])])),['GL01','L21','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([foot(c,[a,b]),euler(c,[a,b])])),['GL01','L21','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),midpoint([b,c])])),['GL01','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),midpoint([a,c])])),['GL01','L22','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),midpoint([a,b])])),['GL01','L22','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),foot(a,[b,c])])),['GL01','L22','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),foot(b,[a,c])])),['GL01','L22','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),foot(c,[a,b])])),['GL01','L22','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),euler(b,[a,c])])),['GL01','L22','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(a,[b,c]),euler(c,[a,b])])),['GL01','L22','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),midpoint([b,c])])),['GL01','L23','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),midpoint([a,c])])),['GL01','L23','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),midpoint([a,b])])),['GL01','L23','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),foot(a,[b,c])])),['GL01','L23','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),foot(b,[a,c])])),['GL01','L23','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),foot(c,[a,b])])),['GL01','L23','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),euler(a,[b,c])])),['GL01','L23','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(b,[a,c]),euler(c,[a,b])])),['GL01','L23','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),midpoint([b,c])])),['GL01','L24','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),midpoint([a,c])])),['GL01','L24','L17','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),midpoint([a,b])])),['GL01','L24','L18','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),foot(a,[b,c])])),['GL01','L24','L19','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),foot(b,[a,c])])),['GL01','L24','L20','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),foot(c,[a,b])])),['GL01','L24','L21','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),euler(a,[b,c])])),['GL01','L24','L22','D32']).
derived_lemma(inc(npcenter([a,b],c),side_bis([euler(c,[a,b]),euler(b,[a,c])])),['GL01','L24','L23','D32']).
derived_lemma(inc(angle_bis_foot(a,[b,c]),side_bis([foot(angle_bis_foot(a,[b,c]),line([a,c])),foot(angle_bis_foot(a,[b,c]),line([a,b]))])),['GL01','L28','GD02']).
derived_lemma(inc(angle_bis_foot(b,[a,c]),side_bis([foot(angle_bis_foot(b,[a,c]),line([b,c])),foot(angle_bis_foot(b,[a,c]),line([a,b]))])),['GL01','L29','GD02']).
derived_lemma(inc(angle_bis_foot(c,[a,b]),side_bis([foot(angle_bis_foot(c,[a,b]),line([b,c])),foot(angle_bis_foot(c,[a,b]),line([a,c]))])),['GL01','L30','GD02']).
derived_lemma(inc(point_n(a,[b,c]),side_bis([b,incenter([a,b],c)])),['GL01','L31','L32','GD02']).
derived_lemma(inc(point_n(a,[b,c]),side_bis([incenter([a,b],c),c])),['GL01','L32','GD02']).
derived_lemma(inc(point_n(a,[b,c]),side_bis([incenter([a,b],c),b])),['GL01','L32','L31','GD02']).
derived_lemma(inc(point_n(b,[a,c]),side_bis([c,a])),['GL01','L33','GD02']).
derived_lemma(inc(point_n(b,[a,c]),side_bis([c,incenter([a,b],c)])),['GL01','L33','L34','GD02']).
derived_lemma(inc(point_n(b,[a,c]),side_bis([incenter([a,b],c),a])),['GL01','L34','GD02']).
derived_lemma(inc(point_n(b,[a,c]),side_bis([incenter([a,b],c),c])),['GL01','L34','L33','GD02']).
derived_lemma(inc(point_n(c,[a,b]),side_bis([a,incenter([a,b],c)])),['GL01','L35','L36','GD02']).
derived_lemma(inc(point_n(c,[a,b]),side_bis([incenter([a,b],c),b])),['GL01','L36','GD02']).
derived_lemma(inc(point_n(c,[a,b]),side_bis([incenter([a,b],c),a])),['GL01','L36','L35','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([c,b])),['GL01','L37','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([c,foot(b,[a,c])])),['GL01','L37','L38','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([c,foot(c,[a,b])])),['GL01','L37','L39','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(b,[a,c]),b])),['GL01','L38','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(b,[a,c]),c])),['GL01','L38','L37','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(b,[a,c]),foot(c,[a,b])])),['GL01','L38','L39','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(c,[a,b]),b])),['GL01','L39','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(c,[a,b]),c])),['GL01','L39','L37','GD02']).
derived_lemma(inc(midpoint([b,c]),side_bis([foot(c,[a,b]),foot(b,[a,c])])),['GL01','L39','L38','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([b,a])),['GL01','L40','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([b,foot(b,[a,c])])),['GL01','L40','L41','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([b,foot(a,[b,c])])),['GL01','L40','L42','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(b,[a,c]),a])),['GL01','L41','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(b,[a,c]),b])),['GL01','L41','L40','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(b,[a,c]),foot(a,[b,c])])),['GL01','L41','L42','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(a,[b,c]),a])),['GL01','L42','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(a,[b,c]),b])),['GL01','L42','L40','GD02']).
derived_lemma(inc(midpoint([a,b]),side_bis([foot(a,[b,c]),foot(b,[a,c])])),['GL01','L42','L41','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([a,foot(a,[b,c])])),['GL01','L43','L44','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([a,foot(c,[a,b])])),['GL01','L43','L45','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(a,[b,c]),c])),['GL01','L44','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(a,[b,c]),a])),['GL01','L44','L43','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(a,[b,c]),foot(c,[a,b])])),['GL01','L44','L45','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(c,[a,b]),c])),['GL01','L45','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(c,[a,b]),a])),['GL01','L45','L43','GD02']).
derived_lemma(inc(midpoint([a,c]),side_bis([foot(c,[a,b]),foot(a,[b,c])])),['GL01','L45','L44','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([orthocenter([a,b],c),a])),['GL01','L46','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([orthocenter([a,b],c),foot(b,[a,c])])),['GL01','L46','L47','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([orthocenter([a,b],c),foot(c,[a,b])])),['GL01','L46','L48','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(b,[a,c]),a])),['GL01','L47','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(b,[a,c]),orthocenter([a,b],c)])),['GL01','L47','L46','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(b,[a,c]),foot(c,[a,b])])),['GL01','L47','L48','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(c,[a,b]),a])),['GL01','L48','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(c,[a,b]),orthocenter([a,b],c)])),['GL01','L48','L46','GD02']).
derived_lemma(inc(euler(a,[b,c]),side_bis([foot(c,[a,b]),foot(b,[a,c])])),['GL01','L48','L47','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([orthocenter([a,b],c),b])),['GL01','L49','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([orthocenter([a,b],c),foot(a,[b,c])])),['GL01','L49','L50','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([orthocenter([a,b],c),foot(c,[a,b])])),['GL01','L49','L51','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(a,[b,c]),b])),['GL01','L50','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(a,[b,c]),orthocenter([a,b],c)])),['GL01','L50','L49','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(a,[b,c]),foot(c,[a,b])])),['GL01','L50','L51','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(c,[a,b]),b])),['GL01','L51','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(c,[a,b]),orthocenter([a,b],c)])),['GL01','L51','L49','GD02']).
derived_lemma(inc(euler(b,[a,c]),side_bis([foot(c,[a,b]),foot(a,[b,c])])),['GL01','L51','L50','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([orthocenter([a,b],c),c])),['GL01','L52','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([orthocenter([a,b],c),foot(b,[a,c])])),['GL01','L52','L53','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([orthocenter([a,b],c),foot(a,[b,c])])),['GL01','L52','L54','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(b,[a,c]),c])),['GL01','L53','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(b,[a,c]),orthocenter([a,b],c)])),['GL01','L53','L52','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(b,[a,c]),foot(a,[b,c])])),['GL01','L53','L54','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(a,[b,c]),c])),['GL01','L54','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(a,[b,c]),orthocenter([a,b],c)])),['GL01','L54','L52','GD02']).
derived_lemma(inc(euler(c,[a,b]),side_bis([foot(a,[b,c]),foot(b,[a,c])])),['GL01','L54','L53','GD02']).
derived_lemma(inc(a,homothety(midpoint([a,b]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1)),['GL02','D20','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,b]),line([b,c]),-1,1)),['GL02','D20','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,b]),line([a,b]),-1,1)),['GL02','D20','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,b]),altitude(b,[a,c]),-1,1)),['GL02','D20','D9']).
derived_lemma(inc(a,homothety(midpoint([a,b]),median(b,[a,c]),-1,1)),['GL02','D20','D18']).
derived_lemma(inc(a,homothety(midpoint([a,b]),angle_bis(b,[a,c]),-1,1)),['GL02','D20','L6']).
derived_lemma(inc(b,homothety(midpoint([b,c]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1)),['GL02','D21','GD01']).
derived_lemma(inc(b,homothety(midpoint([b,c]),line([a,c]),-1,1)),['GL02','D21','GD01']).
derived_lemma(inc(b,homothety(midpoint([b,c]),line([b,c]),-1,1)),['GL02','D21','GD01']).
derived_lemma(inc(b,homothety(midpoint([b,c]),altitude(c,[a,b]),-1,1)),['GL02','D21','D10']).
derived_lemma(inc(b,homothety(midpoint([b,c]),median(c,[a,b]),-1,1)),['GL02','D21','D19']).
derived_lemma(inc(b,homothety(midpoint([b,c]),angle_bis(c,[a,b]),-1,1)),['GL02','D21','L7']).
derived_lemma(inc(c,homothety(midpoint([a,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1)),['GL02','D22','GD01']).
derived_lemma(inc(c,homothety(midpoint([a,c]),line([a,c]),-1,1)),['GL02','D22','GD01']).
derived_lemma(inc(c,homothety(midpoint([a,c]),line([a,b]),-1,1)),['GL02','D22','GD01']).
derived_lemma(inc(c,homothety(midpoint([a,c]),altitude(a,[b,c]),-1,1)),['GL02','D22','D8']).
derived_lemma(inc(c,homothety(midpoint([a,c]),median(a,[b,c]),-1,1)),['GL02','D22','D17']).
derived_lemma(inc(c,homothety(midpoint([a,c]),angle_bis(a,[b,c]),-1,1)),['GL02','D22','L5']).
derived_lemma(inc(a,homothety(euler(a,[b,c]),altitude(a,[b,c]),-1,1)),['GL02','D28','D3']).
derived_lemma(inc(a,homothety(euler(a,[b,c]),altitude(b,[a,c]),-1,1)),['GL02','D28','D3']).
derived_lemma(inc(a,homothety(euler(a,[b,c]),altitude(c,[a,b]),-1,1)),['GL02','D28','L3']).
derived_lemma(inc(b,homothety(euler(b,[a,c]),altitude(a,[b,c]),-1,1)),['GL02','D29','D3']).
derived_lemma(inc(b,homothety(euler(b,[a,c]),altitude(b,[a,c]),-1,1)),['GL02','D29','D3']).
derived_lemma(inc(b,homothety(euler(b,[a,c]),altitude(c,[a,b]),-1,1)),['GL02','D29','L3']).
derived_lemma(inc(c,homothety(euler(c,[a,b]),altitude(a,[b,c]),-1,1)),['GL02','D30','D3']).
derived_lemma(inc(c,homothety(euler(c,[a,b]),altitude(b,[a,c]),-1,1)),['GL02','D30','D3']).
derived_lemma(inc(c,homothety(euler(c,[a,b]),altitude(c,[a,b]),-1,1)),['GL02','D30','L3']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b,c]),-1,1)),['GL02','D31','D1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a,c]),-1,1)),['GL02','D31','D1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a,b]),-1,1)),['GL02','D31','L1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c,a_k]),-1,1)),['GL02','D31','GL01','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c,b_k]),-1,1)),['GL02','D31','GL01','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c,c_k]),-1,1)),['GL02','D31','GL01','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c,a]),-1,1)),['GL02','D31','GL01','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c,b]),-1,1)),['GL02','D31','GL01','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,c]),-1,1)),['GL02','D31','GL01','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,b_k]),-1,1)),['GL02','D31','GL01','D38','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,c_k]),-1,1)),['GL02','D31','GL01','D38','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,a]),-1,1)),['GL02','D31','GL01','D38','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,b]),-1,1)),['GL02','D31','GL01','D38','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,c]),-1,1)),['GL02','D31','GL01','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,a_k]),-1,1)),['GL02','D31','GL01','D39','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,c_k]),-1,1)),['GL02','D31','GL01','D39','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,a]),-1,1)),['GL02','D31','GL01','D39','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,b]),-1,1)),['GL02','D31','GL01','D39','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,c]),-1,1)),['GL02','D31','GL01','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,a_k]),-1,1)),['GL02','D31','GL01','D40','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,b_k]),-1,1)),['GL02','D31','GL01','D40','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,a]),-1,1)),['GL02','D31','GL01','D40','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,b]),-1,1)),['GL02','D31','GL01','D40','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a,a_k]),-1,1)),['GL02','D31','GL01','L11','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a,b_k]),-1,1)),['GL02','D31','GL01','L11','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([a,c_k]),-1,1)),['GL02','D31','GL01','L11','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b,a_k]),-1,1)),['GL02','D31','GL01','L12','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b,b_k]),-1,1)),['GL02','D31','GL01','L12','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b,c_k]),-1,1)),['GL02','D31','GL01','L12','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),side_bis([b,a]),-1,1)),['GL02','D31','GL01','L12','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,c]),-1,2)),['GL02','L15','D1']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,c]),-1,2)),['GL02','L15','D1']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,b]),-1,2)),['GL02','L15','L1']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,a_k]),-1,2)),['GL02','L15','GL01','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,b_k]),-1,2)),['GL02','L15','GL01','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,c_k]),-1,2)),['GL02','L15','GL01','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,a]),-1,2)),['GL02','L15','GL01','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,b]),-1,2)),['GL02','L15','GL01','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,c]),-1,2)),['GL02','L15','GL01','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,b_k]),-1,2)),['GL02','L15','GL01','D38','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,c_k]),-1,2)),['GL02','L15','GL01','D38','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,a]),-1,2)),['GL02','L15','GL01','D38','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,b]),-1,2)),['GL02','L15','GL01','D38','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,c]),-1,2)),['GL02','L15','GL01','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,a_k]),-1,2)),['GL02','L15','GL01','D39','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,c_k]),-1,2)),['GL02','L15','GL01','D39','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,a]),-1,2)),['GL02','L15','GL01','D39','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,b]),-1,2)),['GL02','L15','GL01','D39','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,c]),-1,2)),['GL02','L15','GL01','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,a_k]),-1,2)),['GL02','L15','GL01','D40','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,b_k]),-1,2)),['GL02','L15','GL01','D40','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,a]),-1,2)),['GL02','L15','GL01','D40','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,b]),-1,2)),['GL02','L15','GL01','D40','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,a_k]),-1,2)),['GL02','L15','GL01','L11','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,b_k]),-1,2)),['GL02','L15','GL01','L11','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,c_k]),-1,2)),['GL02','L15','GL01','L11','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,a_k]),-1,2)),['GL02','L15','GL01','L12','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,b_k]),-1,2)),['GL02','L15','GL01','L12','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,c_k]),-1,2)),['GL02','L15','GL01','L12','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,a]),-1,2)),['GL02','L15','GL01','L12','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),median(a,[b,c]),-3,1)),['GL02','L16','D4']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),median(b,[a,c]),-3,1)),['GL02','L16','D4']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),median(c,[a,b]),-3,1)),['GL02','L16','L4']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([b,c]),-2,1)),['GL02','L55','D11']).
derived_lemma(inc(a,homothety(centroid([a,b],c),line_x1,-2,1)),['GL02','L55','D85']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL02','L55','GL01','L38','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([b,foot(c,[a,b])]),-2,1)),['GL02','L55','GL01','L39','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL02','L55','GL01','L37','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([c,foot(b,[a,c])]),-2,1)),['GL02','L55','GL01','L37','L38','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL02','L55','GL01','L37','L39','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL02','L55','GL01','L38','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),c]),-2,1)),['GL02','L55','GL01','L38','L37','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),-2,1)),['GL02','L55','GL01','L38','L39','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),b]),-2,1)),['GL02','L55','GL01','L39','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL02','L55','GL01','L39','L37','GD02']).
derived_lemma(inc(a,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),-2,1)),['GL02','L55','GL01','L39','L38','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([a,c]),-2,1)),['GL02','L56','D12']).
derived_lemma(inc(b,homothety(centroid([a,b],c),line_x2,-2,1)),['GL02','L56','D86']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL02','L56','GL01','L43','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([c,foot(a,[b,c])]),-2,1)),['GL02','L56','GL01','L44','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL02','L56','GL01','L45','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL02','L56','GL01','L43','L44','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([a,foot(c,[a,b])]),-2,1)),['GL02','L56','GL01','L43','L45','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),c]),-2,1)),['GL02','L56','GL01','L44','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL02','L56','GL01','L44','L43','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),-2,1)),['GL02','L56','GL01','L44','L45','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL02','L56','GL01','L45','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),a]),-2,1)),['GL02','L56','GL01','L45','L43','GD02']).
derived_lemma(inc(b,homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),-2,1)),['GL02','L56','GL01','L45','L44','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([a,b]),-2,1)),['GL02','L57','D13']).
derived_lemma(inc(c,homothety(centroid([a,b],c),line_x3,-2,1)),['GL02','L57','D87']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([a,foot(b,[a,c])]),-2,1)),['GL02','L57','GL01','L41','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL02','L57','GL01','L42','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL02','L57','GL01','L40','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL02','L57','GL01','L40','L41','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([b,foot(a,[b,c])]),-2,1)),['GL02','L57','GL01','L40','L42','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),a]),-2,1)),['GL02','L57','GL01','L41','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL02','L57','GL01','L41','L40','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),-2,1)),['GL02','L57','GL01','L41','L42','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL02','L57','GL01','L42','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),b]),-2,1)),['GL02','L57','GL01','L42','L40','GD02']).
derived_lemma(inc(c,homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),-2,1)),['GL02','L57','GL01','L42','L41','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,c]),-2,1)),['GL02','L58','D1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,c]),-2,1)),['GL02','L58','D1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,b]),-2,1)),['GL02','L58','L1']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,a_k]),-2,1)),['GL02','L58','GL01','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,b_k]),-2,1)),['GL02','L58','GL01','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,c_k]),-2,1)),['GL02','L58','GL01','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL02','L58','GL01','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL02','L58','GL01','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,c]),-2,1)),['GL02','L58','GL01','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,b_k]),-2,1)),['GL02','L58','GL01','D38','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,c_k]),-2,1)),['GL02','L58','GL01','D38','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,a]),-2,1)),['GL02','L58','GL01','D38','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a_k,b]),-2,1)),['GL02','L58','GL01','D38','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,c]),-2,1)),['GL02','L58','GL01','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,a_k]),-2,1)),['GL02','L58','GL01','D39','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,c_k]),-2,1)),['GL02','L58','GL01','D39','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,a]),-2,1)),['GL02','L58','GL01','D39','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b_k,b]),-2,1)),['GL02','L58','GL01','D39','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,c]),-2,1)),['GL02','L58','GL01','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,a_k]),-2,1)),['GL02','L58','GL01','D40','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,b_k]),-2,1)),['GL02','L58','GL01','D40','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,a]),-2,1)),['GL02','L58','GL01','D40','L11','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([c_k,b]),-2,1)),['GL02','L58','GL01','D40','L12','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,a_k]),-2,1)),['GL02','L58','GL01','L11','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,b_k]),-2,1)),['GL02','L58','GL01','L11','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([a,c_k]),-2,1)),['GL02','L58','GL01','L11','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,a_k]),-2,1)),['GL02','L58','GL01','L12','D38','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,b_k]),-2,1)),['GL02','L58','GL01','L12','D39','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,c_k]),-2,1)),['GL02','L58','GL01','L12','D40','D26']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL02','L58','GL01','L12','L11','D26']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(midpoint([b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1)),['GL02','L62','GD01']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(midpoint([a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1)),['GL02','L63','GD01']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(midpoint([a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1)),['GL02','L64','GD01']).
derived_lemma(sratio(a,b,a,midpoint([a,b]),2,1),['GL03','D20']).
derived_lemma(inc(a,homothety(b,side_bis([a,b]),2,1)),['GL02','GL03','D20','D13']).
derived_lemma(inc(a,homothety(b,median(c,[a,b]),2,1)),['GL02','GL03','D20','D19']).
derived_lemma(inc(a,homothety(b,line_x3,2,1)),['GL02','GL03','D20','D87']).
derived_lemma(inc(c,homothety(midpoint([a,c]),homothety(b,line_x3,2,1),-1,1)),['D22','GL02','GL03','D20','D87']).
derived_lemma(inc(a,homothety(b,side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','D20','GL01','L41','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','D20','GL01','L42','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([b,a]),2,1)),['GL02','GL03','D20','GL01','L40','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','D20','GL01','L40','L41','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','D20','GL01','L40','L42','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','D20','GL01','L41','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','D20','GL01','L41','L40','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','D20','GL01','L41','L42','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','D20','GL01','L42','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','D20','GL01','L42','L40','GD02']).
derived_lemma(inc(a,homothety(b,side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','D20','GL01','L42','L41','GD02']).
derived_lemma(sratio(b,c,b,midpoint([b,c]),2,1),['GL03','D21']).
derived_lemma(inc(b,homothety(c,side_bis([b,c]),2,1)),['GL02','GL03','D21','D11']).
derived_lemma(inc(b,homothety(c,median(a,[b,c]),2,1)),['GL02','GL03','D21','D17']).
derived_lemma(inc(b,homothety(c,line_x1,2,1)),['GL02','GL03','D21','D85']).
derived_lemma(inc(a,homothety(midpoint([a,b]),homothety(c,line_x1,2,1),-1,1)),['D20','GL02','GL03','D21','D85']).
derived_lemma(inc(b,homothety(c,side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','D21','GL01','L38','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','D21','GL01','L39','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([c,b]),2,1)),['GL02','GL03','D21','GL01','L37','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','D21','GL01','L37','L38','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','D21','GL01','L38','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','D21','GL01','L38','L37','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D21','GL01','L38','L39','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','D21','GL01','L39','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(inc(b,homothety(c,side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','D21','GL01','L39','L38','GD02']).
derived_lemma(sratio(c,a,c,midpoint([a,c]),2,1),['GL03','D22']).
derived_lemma(inc(c,homothety(a,side_bis([a,c]),2,1)),['GL02','GL03','D22','D12']).
derived_lemma(inc(c,homothety(a,median(b,[a,c]),2,1)),['GL02','GL03','D22','D18']).
derived_lemma(inc(c,homothety(a,line_x2,2,1)),['GL02','GL03','D22','D86']).
derived_lemma(inc(b,homothety(midpoint([b,c]),homothety(a,line_x2,2,1),-1,1)),['D21','GL02','GL03','D22','D86']).
derived_lemma(inc(c,homothety(a,side_bis([c,a]),2,1)),['GL02','GL03','D22','GL01','L43','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','D22','GL01','L44','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','D22','GL01','L45','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','D22','GL01','L43','L45','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','D22','GL01','L44','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D22','GL01','L44','L45','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','D22','GL01','L45','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','D22','GL01','L45','L43','GD02']).
derived_lemma(inc(c,homothety(a,side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','D22','GL01','L45','L44','GD02']).
derived_lemma(sratio(a,orthocenter([a,b],c),a,euler(a,[b,c]),2,1),['GL03','D28']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','D28','GL01','L47','GD02']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','D28','GL01','L48','GD02']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','D28','GL01','L47','GD02']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D28','GL01','L47','L48','GD02']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','D28','GL01','L48','GD02']).
derived_lemma(inc(a,homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','D28','GL01','L48','L47','GD02']).
derived_lemma(sratio(b,orthocenter([a,b],c),b,euler(b,[a,c]),2,1),['GL03','D29']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','D29','GL01','L50','GD02']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','D29','GL01','L51','GD02']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','D29','GL01','L50','GD02']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D29','GL01','L50','L51','GD02']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','D29','GL01','L51','GD02']).
derived_lemma(inc(b,homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','D29','GL01','L51','L50','GD02']).
derived_lemma(sratio(c,orthocenter([a,b],c),c,euler(c,[a,b]),2,1),['GL03','D30']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','D30','GL01','L53','GD02']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','D30','GL01','L54','GD02']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','D30','GL01','L53','GD02']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','D30','GL01','L53','L54','GD02']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','D30','GL01','L54','GD02']).
derived_lemma(inc(c,homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','D30','GL01','L54','L53','GD02']).
derived_lemma(sratio(orthocenter([a,b],c),circumcenter([a,b],c),orthocenter([a,b],c),npcenter([a,b],c),2,1),['GL03','D31']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','D31','GL01','L19','L20','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D31','GL01','L19','L21','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','D31','GL01','L20','L19','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','D31','GL01','L20','L21','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','D31','GL01','L21','L19','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','D31','GL01','L21','L20','D32']).
derived_lemma(sratio(npcenter([a,b],c),circumcenter([a,b],c),npcenter([a,b],c),centroid([a,b],c),3,1),['GL03','L15']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),median(a,[b,c]),3,2)),['GL02','GL03','L15','D4']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),median(b,[a,c]),3,2)),['GL02','GL03','L15','D4']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),median(c,[a,b]),3,2)),['GL02','GL03','L15','L4']).
derived_lemma(sratio(orthocenter([a,b],c),centroid([a,b],c),orthocenter([a,b],c),npcenter([a,b],c),4,3),['GL03','L16']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),4,1)),['GL02','GL03','L16','GL01','L19','L20','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),4,1)),['GL02','GL03','L16','GL01','L19','L21','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),4,1)),['GL02','GL03','L16','GL01','L20','L19','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),4,1)),['GL02','GL03','L16','GL01','L20','L21','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),4,1)),['GL02','GL03','L16','GL01','L21','L19','D32']).
derived_lemma(inc(orthocenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),4,1)),['GL02','GL03','L16','GL01','L21','L20','D32']).
derived_lemma(sratio(a,midpoint([b,c]),a,centroid([a,b],c),3,2),['GL03','L55']).
derived_lemma(inc(a,homothety(midpoint([b,c]),median(b,[a,c]),3,1)),['GL02','GL03','L55','D4']).
derived_lemma(inc(a,homothety(midpoint([b,c]),median(c,[a,b]),3,1)),['GL02','GL03','L55','L4']).
derived_lemma(sratio(b,midpoint([a,c]),b,centroid([a,b],c),3,2),['GL03','L56']).
derived_lemma(inc(b,homothety(midpoint([a,c]),median(a,[b,c]),3,1)),['GL02','GL03','L56','D4']).
derived_lemma(inc(b,homothety(midpoint([a,c]),median(c,[a,b]),3,1)),['GL02','GL03','L56','L4']).
derived_lemma(sratio(c,midpoint([a,b]),c,centroid([a,b],c),3,2),['GL03','L57']).
derived_lemma(inc(c,homothety(midpoint([a,b]),median(a,[b,c]),3,1)),['GL02','GL03','L57','D4']).
derived_lemma(inc(c,homothety(midpoint([a,b]),median(b,[a,c]),3,1)),['GL02','GL03','L57','D4']).
derived_lemma(sratio(orthocenter([a,b],c),circumcenter([a,b],c),orthocenter([a,b],c),centroid([a,b],c),3,2),['GL03','L58']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),median(a,[b,c]),3,1)),['GL02','GL03','L58','D4']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),median(b,[a,c]),3,1)),['GL02','GL03','L58','D4']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),median(c,[a,b]),3,1)),['GL02','GL03','L58','L4']).
derived_lemma(sratio(foot(incenter([a,b],c),[b,c]),foot(outcenter(a,[b,c]),[b,c]),foot(incenter([a,b],c),[b,c]),midpoint([b,c]),2,1),['GL03','L62']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([b,c]),2,1)),['GL02','GL03','L62','D11']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),median(a,[b,c]),2,1)),['GL02','GL03','L62','D17']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),line_x1,2,1)),['GL02','GL03','L62','D85']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','L62','GL01','L38','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','L62','GL01','L39','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([c,b]),2,1)),['GL02','GL03','L62','GL01','L37','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','L62','GL01','L37','L38','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','L62','GL01','L37','L39','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','L62','GL01','L38','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','L62','GL01','L38','L37','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','L62','GL01','L38','L39','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','L62','GL01','L39','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','L62','GL01','L39','L37','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','L62','GL01','L39','L38','GD02']).
derived_lemma(sratio(foot(incenter([a,b],c),[a,c]),foot(outcenter(b,[a,c]),[a,c]),foot(incenter([a,b],c),[a,c]),midpoint([a,c]),2,1),['GL03','L63']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([a,c]),2,1)),['GL02','GL03','L63','D12']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),median(b,[a,c]),2,1)),['GL02','GL03','L63','D18']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),line_x2,2,1)),['GL02','GL03','L63','D86']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([c,a]),2,1)),['GL02','GL03','L63','GL01','L43','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','L63','GL01','L44','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','L63','GL01','L45','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','L63','GL01','L43','L44','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','L63','GL01','L43','L45','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','L63','GL01','L44','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','L63','GL01','L44','L43','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','L63','GL01','L44','L45','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','L63','GL01','L45','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','L63','GL01','L45','L43','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','L63','GL01','L45','L44','GD02']).
derived_lemma(sratio(foot(incenter([a,b],c),[a,b]),foot(outcenter(c,[a,b]),[a,b]),foot(incenter([a,b],c),[a,b]),midpoint([a,b]),2,1),['GL03','L64']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([a,b]),2,1)),['GL02','GL03','L64','D13']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),median(c,[a,b]),2,1)),['GL02','GL03','L64','D19']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),line_x3,2,1)),['GL02','GL03','L64','D87']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','L64','GL01','L41','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','L64','GL01','L42','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([b,a]),2,1)),['GL02','GL03','L64','GL01','L40','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','L64','GL01','L40','L41','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','L64','GL01','L40','L42','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','L64','GL01','L41','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','L64','GL01','L41','L40','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','L64','GL01','L41','L42','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','L64','GL01','L42','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','L64','GL01','L42','L40','GD02']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','L64','GL01','L42','L41','GD02']).
derived_lemma(sratio(b,midpoint([a,b]),b,a,1,2),['GL04','D20']).
derived_lemma(inc(b,homothety(midpoint([a,b]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1)),['GL02','GL04','D20','GD01']).
derived_lemma(inc(b,homothety(midpoint([a,b]),line([a,c]),-1,1)),['GL02','GL04','D20','GD01']).
derived_lemma(inc(b,homothety(midpoint([a,b]),line([a,b]),-1,1)),['GL02','GL04','D20','GD01']).
derived_lemma(inc(b,homothety(midpoint([a,b]),altitude(a,[b,c]),-1,1)),['GL02','GL04','D20','D8']).
derived_lemma(inc(b,homothety(midpoint([a,b]),median(a,[b,c]),-1,1)),['GL02','GL04','D20','D17']).
derived_lemma(inc(b,homothety(midpoint([a,b]),angle_bis(a,[b,c]),-1,1)),['GL02','GL04','D20','L5']).
derived_lemma(inc(b,homothety(midpoint([a,b]),homothety(b,line_x3,2,1),-1,1)),['GL04','GL02','GL03','D20','D87']).
derived_lemma(sratio(b,a,b,midpoint([a,b]),2,1),['GL03','GL04','D20']).
derived_lemma(inc(b,homothety(a,side_bis([a,b]),2,1)),['GL02','GL03','GL04','D20','D13']).
derived_lemma(inc(b,homothety(a,median(c,[a,b]),2,1)),['GL02','GL03','GL04','D20','D19']).
derived_lemma(inc(b,homothety(a,line_x3,2,1)),['GL02','GL03','GL04','D20','D87']).
derived_lemma(inc(a,homothety(midpoint([a,b]),homothety(a,line_x3,2,1),-1,1)),['GL02','GL03','GL04','D20','D87']).
derived_lemma(inc(b,homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L42','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([b,a]),2,1)),['GL02','GL03','GL04','D20','GL01','L40','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L40','L41','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L40','L42','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','GL04','D20','GL01','L41','L40','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L41','L42','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','GL04','D20','GL01','L42','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','GL04','D20','GL01','L42','L40','GD02']).
derived_lemma(inc(b,homothety(a,side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D20','GL01','L42','L41','GD02']).
derived_lemma(sratio(c,midpoint([b,c]),c,b,1,2),['GL04','D21']).
derived_lemma(inc(c,homothety(midpoint([b,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1)),['GL02','GL04','D21','GD01']).
derived_lemma(inc(c,homothety(midpoint([b,c]),line([b,c]),-1,1)),['GL02','GL04','D21','GD01']).
derived_lemma(inc(c,homothety(midpoint([b,c]),line([a,b]),-1,1)),['GL02','GL04','D21','GD01']).
derived_lemma(inc(c,homothety(midpoint([b,c]),altitude(b,[a,c]),-1,1)),['GL02','GL04','D21','D9']).
derived_lemma(inc(c,homothety(midpoint([b,c]),median(b,[a,c]),-1,1)),['GL02','GL04','D21','D18']).
derived_lemma(inc(c,homothety(midpoint([b,c]),angle_bis(b,[a,c]),-1,1)),['GL02','GL04','D21','L6']).
derived_lemma(inc(c,homothety(midpoint([b,c]),homothety(c,line_x1,2,1),-1,1)),['GL04','GL02','GL03','D21','D85']).
derived_lemma(inc(c,homothety(midpoint([b,c]),homothety(a,line_x3,2,1),-1,1)),['D21','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(c,b,c,midpoint([b,c]),2,1),['GL03','GL04','D21']).
derived_lemma(inc(c,homothety(b,side_bis([b,c]),2,1)),['GL02','GL03','GL04','D21','D11']).
derived_lemma(inc(c,homothety(b,median(a,[b,c]),2,1)),['GL02','GL03','GL04','D21','D17']).
derived_lemma(inc(c,homothety(b,line_x1,2,1)),['GL02','GL03','GL04','D21','D85']).
derived_lemma(inc(b,homothety(midpoint([b,c]),homothety(b,line_x1,2,1),-1,1)),['GL02','GL03','GL04','D21','D85']).
derived_lemma(inc(c,homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([c,b]),2,1)),['GL02','GL03','GL04','D21','GL01','L37','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D21','GL01','L37','L38','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D21','GL01','L37','L39','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','GL04','D21','GL01','L38','L37','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D21','GL01','L38','L39','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','GL04','D21','GL01','L39','L37','GD02']).
derived_lemma(inc(c,homothety(b,side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D21','GL01','L39','L38','GD02']).
derived_lemma(sratio(a,midpoint([a,c]),a,c,1,2),['GL04','D22']).
derived_lemma(inc(a,homothety(midpoint([a,c]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1)),['GL02','GL04','D22','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,c]),line([a,c]),-1,1)),['GL02','GL04','D22','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,c]),line([b,c]),-1,1)),['GL02','GL04','D22','GD01']).
derived_lemma(inc(a,homothety(midpoint([a,c]),altitude(c,[a,b]),-1,1)),['GL02','GL04','D22','D10']).
derived_lemma(inc(a,homothety(midpoint([a,c]),median(c,[a,b]),-1,1)),['GL02','GL04','D22','D19']).
derived_lemma(inc(a,homothety(midpoint([a,c]),angle_bis(c,[a,b]),-1,1)),['GL02','GL04','D22','L7']).
derived_lemma(inc(a,homothety(midpoint([a,c]),homothety(a,line_x2,2,1),-1,1)),['GL04','GL02','GL03','D22','D86']).
derived_lemma(inc(a,homothety(midpoint([a,c]),homothety(b,line_x1,2,1),-1,1)),['D22','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(a,c,a,midpoint([a,c]),2,1),['GL03','GL04','D22']).
derived_lemma(inc(a,homothety(c,side_bis([a,c]),2,1)),['GL02','GL03','GL04','D22','D12']).
derived_lemma(inc(a,homothety(c,median(b,[a,c]),2,1)),['GL02','GL03','GL04','D22','D18']).
derived_lemma(inc(a,homothety(c,line_x2,2,1)),['GL02','GL03','GL04','D22','D86']).
derived_lemma(inc(c,homothety(midpoint([a,c]),homothety(c,line_x2,2,1),-1,1)),['GL02','GL03','GL04','D22','D86']).
derived_lemma(inc(b,homothety(midpoint([a,b]),homothety(c,line_x2,2,1),-1,1)),['D20','GL02','GL03','GL04','D22','D86']).
derived_lemma(inc(a,homothety(c,side_bis([c,a]),2,1)),['GL02','GL03','GL04','D22','GL01','L43','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D22','GL01','L45','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D22','GL01','L43','L44','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D22','GL01','L43','L45','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','GL04','D22','GL01','L44','L43','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D22','GL01','L44','L45','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','GL04','D22','GL01','L45','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','GL04','D22','GL01','L45','L43','GD02']).
derived_lemma(inc(a,homothety(c,side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D22','GL01','L45','L44','GD02']).
derived_lemma(sratio(orthocenter([a,b],c),euler(a,[b,c]),orthocenter([a,b],c),a,1,2),['GL04','D28']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1)),['GL02','GL04','D28','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),line([a,c]),-1,1)),['GL02','GL04','D28','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),line([a,b]),-1,1)),['GL02','GL04','D28','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),altitude(a,[b,c]),-1,1)),['GL02','GL04','D28','D8']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),median(a,[b,c]),-1,1)),['GL02','GL04','D28','D17']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),angle_bis(a,[b,c]),-1,1)),['GL02','GL04','D28','L5']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),homothety(b,line_x3,2,1),-1,1)),['GL04','D28','GL02','GL03','D20','D87']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(a,[b,c]),homothety(c,line_x2,2,1),-1,1)),['D28','GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(orthocenter([a,b],c),a,orthocenter([a,b],c),euler(a,[b,c]),2,1),['GL03','GL04','D28']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D28','GL01','L47','L48','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(a,side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D28','GL01','L48','L47','GD02']).
derived_lemma(sratio(orthocenter([a,b],c),euler(b,[a,c]),orthocenter([a,b],c),b,1,2),['GL04','D29']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1)),['GL02','GL04','D29','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),line([b,c]),-1,1)),['GL02','GL04','D29','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),line([a,b]),-1,1)),['GL02','GL04','D29','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),altitude(b,[a,c]),-1,1)),['GL02','GL04','D29','D9']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),median(b,[a,c]),-1,1)),['GL02','GL04','D29','D18']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),angle_bis(b,[a,c]),-1,1)),['GL02','GL04','D29','L6']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),homothety(c,line_x1,2,1),-1,1)),['GL04','D29','GL02','GL03','D21','D85']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(b,[a,c]),homothety(a,line_x3,2,1),-1,1)),['D29','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(orthocenter([a,b],c),b,orthocenter([a,b],c),euler(b,[a,c]),2,1),['GL03','GL04','D29']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D29','GL01','L50','L51','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(b,side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D29','GL01','L51','L50','GD02']).
derived_lemma(sratio(orthocenter([a,b],c),euler(c,[a,b]),orthocenter([a,b],c),c,1,2),['GL04','D30']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1)),['GL02','GL04','D30','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),line([a,c]),-1,1)),['GL02','GL04','D30','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),line([b,c]),-1,1)),['GL02','GL04','D30','GD01']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),altitude(c,[a,b]),-1,1)),['GL02','GL04','D30','D10']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),median(c,[a,b]),-1,1)),['GL02','GL04','D30','D19']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),angle_bis(c,[a,b]),-1,1)),['GL02','GL04','D30','L7']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),homothety(a,line_x2,2,1),-1,1)),['GL04','D30','GL02','GL03','D22','D86']).
derived_lemma(inc(orthocenter([a,b],c),homothety(euler(c,[a,b]),homothety(b,line_x1,2,1),-1,1)),['D30','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(orthocenter([a,b],c),c,orthocenter([a,b],c),euler(c,[a,b]),2,1),['GL03','GL04','D30']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D30','GL01','L53','L54','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(inc(orthocenter([a,b],c),homothety(c,side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D30','GL01','L54','L53','GD02']).
derived_lemma(sratio(circumcenter([a,b],c),npcenter([a,b],c),circumcenter([a,b],c),orthocenter([a,b],c),1,2),['GL04','D31']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),altitude(a,[b,c]),-1,1)),['GL02','GL04','D31','D3']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),altitude(b,[a,c]),-1,1)),['GL02','GL04','D31','D3']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),altitude(c,[a,b]),-1,1)),['GL02','GL04','D31','L3']).
derived_lemma(sratio(circumcenter([a,b],c),orthocenter([a,b],c),circumcenter([a,b],c),npcenter([a,b],c),2,1),['GL03','GL04','D31']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D31','GL01','L19','L20','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D31','GL01','L19','L21','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D31','GL01','L20','L19','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','D31','GL01','L20','L21','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','D31','GL01','L21','L19','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','D31','GL01','L21','L20','D32']).
derived_lemma(sratio(circumcenter([a,b],c),centroid([a,b],c),circumcenter([a,b],c),npcenter([a,b],c),2,3),['GL04','L15']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),-2,1)),['GL02','GL04','L15','GL01','L19','L20','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),-2,1)),['GL02','GL04','L15','GL01','L19','L21','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),-2,1)),['GL02','GL04','L15','GL01','L20','L19','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),-2,1)),['GL02','GL04','L15','GL01','L20','L21','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),-2,1)),['GL02','GL04','L15','GL01','L21','L19','D32']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),-2,1)),['GL02','GL04','L15','GL01','L21','L20','D32']).
derived_lemma(sratio(circumcenter([a,b],c),npcenter([a,b],c),circumcenter([a,b],c),centroid([a,b],c),3,2),['GL03','GL04','L15']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),median(a,[b,c]),3,1)),['GL02','GL03','GL04','L15','D4']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),median(b,[a,c]),3,1)),['GL02','GL03','GL04','L15','D4']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),median(c,[a,b]),3,1)),['GL02','GL03','GL04','L15','L4']).
derived_lemma(sratio(centroid([a,b],c),npcenter([a,b],c),centroid([a,b],c),orthocenter([a,b],c),1,4),['GL04','L16']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),altitude(a,[b,c]),-1,3)),['GL02','GL04','L16','D3']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),altitude(b,[a,c]),-1,3)),['GL02','GL04','L16','D3']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),altitude(c,[a,b]),-1,3)),['GL02','GL04','L16','L3']).
derived_lemma(sratio(centroid([a,b],c),orthocenter([a,b],c),centroid([a,b],c),npcenter([a,b],c),4,1),['GL03','GL04','L16']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),4,3)),['GL02','GL03','GL04','L16','GL01','L19','L20','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),4,3)),['GL02','GL03','GL04','L16','GL01','L19','L21','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),4,3)),['GL02','GL03','GL04','L16','GL01','L20','L19','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),4,3)),['GL02','GL03','GL04','L16','GL01','L20','L21','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),4,3)),['GL02','GL03','GL04','L16','GL01','L21','L19','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),4,3)),['GL02','GL03','GL04','L16','GL01','L21','L20','D32']).
derived_lemma(sratio(midpoint([b,c]),centroid([a,b],c),midpoint([b,c]),a,1,3),['GL04','L55']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,2)),['GL02','GL04','L55','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),line([a,c]),-1,2)),['GL02','GL04','L55','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),line([a,b]),-1,2)),['GL02','GL04','L55','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),altitude(a,[b,c]),-1,2)),['GL02','GL04','L55','D8']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),angle_bis(a,[b,c]),-1,2)),['GL02','GL04','L55','L5']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),homothety(b,line_x3,2,1),-1,2)),['GL04','L55','GL02','GL03','D20','D87']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),homothety(c,line_x2,2,1),-1,2)),['L55','GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(midpoint([b,c]),a,midpoint([b,c]),centroid([a,b],c),3,1),['GL03','GL04','L55']).
derived_lemma(inc(midpoint([b,c]),homothety(a,median(b,[a,c]),3,2)),['GL02','GL03','GL04','L55','D4']).
derived_lemma(inc(midpoint([b,c]),homothety(a,median(c,[a,b]),3,2)),['GL02','GL03','GL04','L55','L4']).
derived_lemma(sratio(midpoint([a,c]),centroid([a,b],c),midpoint([a,c]),b,1,3),['GL04','L56']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,2)),['GL02','GL04','L56','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),line([b,c]),-1,2)),['GL02','GL04','L56','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),line([a,b]),-1,2)),['GL02','GL04','L56','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),altitude(b,[a,c]),-1,2)),['GL02','GL04','L56','D9']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),angle_bis(b,[a,c]),-1,2)),['GL02','GL04','L56','L6']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),homothety(c,line_x1,2,1),-1,2)),['GL04','L56','GL02','GL03','D21','D85']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),homothety(a,line_x3,2,1),-1,2)),['L56','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(midpoint([a,c]),b,midpoint([a,c]),centroid([a,b],c),3,1),['GL03','GL04','L56']).
derived_lemma(inc(midpoint([a,c]),homothety(b,median(a,[b,c]),3,2)),['GL02','GL03','GL04','L56','D4']).
derived_lemma(inc(midpoint([a,c]),homothety(b,median(c,[a,b]),3,2)),['GL02','GL03','GL04','L56','L4']).
derived_lemma(sratio(midpoint([a,b]),centroid([a,b],c),midpoint([a,b]),c,1,3),['GL04','L57']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,2)),['GL02','GL04','L57','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),line([a,c]),-1,2)),['GL02','GL04','L57','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),line([b,c]),-1,2)),['GL02','GL04','L57','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),altitude(c,[a,b]),-1,2)),['GL02','GL04','L57','D10']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),angle_bis(c,[a,b]),-1,2)),['GL02','GL04','L57','L7']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),homothety(a,line_x2,2,1),-1,2)),['GL04','L57','GL02','GL03','D22','D86']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),homothety(b,line_x1,2,1),-1,2)),['L57','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(midpoint([a,b]),c,midpoint([a,b]),centroid([a,b],c),3,1),['GL03','GL04','L57']).
derived_lemma(inc(midpoint([a,b]),homothety(c,median(a,[b,c]),3,2)),['GL02','GL03','GL04','L57','D4']).
derived_lemma(inc(midpoint([a,b]),homothety(c,median(b,[a,c]),3,2)),['GL02','GL03','GL04','L57','D4']).
derived_lemma(sratio(circumcenter([a,b],c),centroid([a,b],c),circumcenter([a,b],c),orthocenter([a,b],c),1,3),['GL04','L58']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),altitude(a,[b,c]),-1,2)),['GL02','GL04','L58','D3']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),altitude(b,[a,c]),-1,2)),['GL02','GL04','L58','D3']).
derived_lemma(inc(circumcenter([a,b],c),homothety(centroid([a,b],c),altitude(c,[a,b]),-1,2)),['GL02','GL04','L58','L3']).
derived_lemma(sratio(circumcenter([a,b],c),orthocenter([a,b],c),circumcenter([a,b],c),centroid([a,b],c),3,1),['GL03','GL04','L58']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),median(a,[b,c]),3,2)),['GL02','GL03','GL04','L58','D4']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),median(b,[a,c]),3,2)),['GL02','GL03','GL04','L58','D4']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),median(c,[a,b]),3,2)),['GL02','GL03','GL04','L58','L4']).
derived_lemma(sratio(foot(outcenter(a,[b,c]),[b,c]),midpoint([b,c]),foot(outcenter(a,[b,c]),[b,c]),foot(incenter([a,b],c),[b,c]),1,2),['GL04','L62']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(midpoint([b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),line_x1,2,1),-1,1)),['GL04','GL02','GL03','L62','D85']).
derived_lemma(sratio(foot(outcenter(a,[b,c]),[b,c]),foot(incenter([a,b],c),[b,c]),foot(outcenter(a,[b,c]),[b,c]),midpoint([b,c]),2,1),['GL03','GL04','L62']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([b,c]),2,1)),['GL02','GL03','GL04','L62','D11']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),median(a,[b,c]),2,1)),['GL02','GL03','GL04','L62','D17']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),line_x1,2,1)),['GL02','GL03','GL04','L62','D85']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(midpoint([b,c]),homothety(foot(incenter([a,b],c),[b,c]),line_x1,2,1),-1,1)),['GL02','GL03','GL04','L62','D85']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L62','GL01','L38','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([b,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L62','GL01','L39','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([c,b]),2,1)),['GL02','GL03','GL04','L62','GL01','L37','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([c,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L62','GL01','L37','L38','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L62','GL01','L37','L39','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','GL04','L62','GL01','L38','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(b,[a,c]),c]),2,1)),['GL02','GL03','GL04','L62','GL01','L38','L37','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L62','GL01','L38','L39','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(c,[a,b]),b]),2,1)),['GL02','GL03','GL04','L62','GL01','L39','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','GL04','L62','GL01','L39','L37','GD02']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L62','GL01','L39','L38','GD02']).
derived_lemma(sratio(foot(outcenter(b,[a,c]),[a,c]),midpoint([a,c]),foot(outcenter(b,[a,c]),[a,c]),foot(incenter([a,b],c),[a,c]),1,2),['GL04','L63']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(midpoint([a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),line_x2,2,1),-1,1)),['GL04','GL02','GL03','L63','D86']).
derived_lemma(sratio(foot(outcenter(b,[a,c]),[a,c]),foot(incenter([a,b],c),[a,c]),foot(outcenter(b,[a,c]),[a,c]),midpoint([a,c]),2,1),['GL03','GL04','L63']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([a,c]),2,1)),['GL02','GL03','GL04','L63','D12']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),median(b,[a,c]),2,1)),['GL02','GL03','GL04','L63','D18']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),line_x2,2,1)),['GL02','GL03','GL04','L63','D86']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(midpoint([a,c]),homothety(foot(incenter([a,b],c),[a,c]),line_x2,2,1),-1,1)),['GL02','GL03','GL04','L63','D86']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([c,a]),2,1)),['GL02','GL03','GL04','L63','GL01','L43','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([c,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L63','GL01','L44','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([c,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L63','GL01','L45','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L63','GL01','L43','L44','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([a,foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L63','GL01','L43','L45','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(a,[b,c]),c]),2,1)),['GL02','GL03','GL04','L63','GL01','L44','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','GL04','L63','GL01','L44','L43','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL02','GL03','GL04','L63','GL01','L44','L45','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(c,[a,b]),c]),2,1)),['GL02','GL03','GL04','L63','GL01','L45','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(c,[a,b]),a]),2,1)),['GL02','GL03','GL04','L63','GL01','L45','L43','GD02']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L63','GL01','L45','L44','GD02']).
derived_lemma(sratio(foot(outcenter(c,[a,b]),[a,b]),midpoint([a,b]),foot(outcenter(c,[a,b]),[a,b]),foot(incenter([a,b],c),[a,b]),1,2),['GL04','L64']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(midpoint([a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),line_x3,2,1),-1,1)),['GL04','GL02','GL03','L64','D87']).
derived_lemma(sratio(foot(outcenter(c,[a,b]),[a,b]),foot(incenter([a,b],c),[a,b]),foot(outcenter(c,[a,b]),[a,b]),midpoint([a,b]),2,1),['GL03','GL04','L64']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([a,b]),2,1)),['GL02','GL03','GL04','L64','D13']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),median(c,[a,b]),2,1)),['GL02','GL03','GL04','L64','D19']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),line_x3,2,1)),['GL02','GL03','GL04','L64','D87']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(midpoint([a,b]),homothety(foot(incenter([a,b],c),[a,b]),line_x3,2,1),-1,1)),['GL02','GL03','GL04','L64','D87']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([a,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L41','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([a,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L42','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([b,a]),2,1)),['GL02','GL03','GL04','L64','GL01','L40','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([b,foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L40','L41','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([b,foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L40','L42','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(b,[a,c]),a]),2,1)),['GL02','GL03','GL04','L64','GL01','L41','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(b,[a,c]),b]),2,1)),['GL02','GL03','GL04','L64','GL01','L41','L40','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L41','L42','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(a,[b,c]),a]),2,1)),['GL02','GL03','GL04','L64','GL01','L42','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(a,[b,c]),b]),2,1)),['GL02','GL03','GL04','L64','GL01','L42','L40','GD02']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL02','GL03','GL04','L64','GL01','L42','L41','GD02']).
derived_lemma(sratio(midpoint([a,b]),b,midpoint([a,b]),a,-1,1),['GL04','GL03','D20']).
derived_lemma(inc(midpoint([a,b]),homothety(b,line([a,foot(outcenter(a,[b,c]),[b,c])]),1,2)),['GL02','GL04','GL03','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(b,line([a,c]),1,2)),['GL02','GL04','GL03','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(b,altitude(a,[b,c]),1,2)),['GL02','GL04','GL03','D20','D8']).
derived_lemma(inc(midpoint([a,b]),homothety(b,median(a,[b,c]),1,2)),['GL02','GL04','GL03','D20','D17']).
derived_lemma(inc(midpoint([a,b]),homothety(b,angle_bis(a,[b,c]),1,2)),['GL02','GL04','GL03','D20','L5']).
derived_lemma(inc(midpoint([a,b]),homothety(b,homothety(b,line_x3,2,1),1,2)),['GL04','GL02','GL03','D20','D87']).
derived_lemma(inc(midpoint([a,b]),homothety(b,homothety(c,line_x2,2,1),1,2)),['D20','GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(midpoint([a,b]),a,midpoint([a,b]),b,-1,1),['GL04','GL03','D20']).
derived_lemma(inc(midpoint([a,b]),homothety(a,line([b,foot(outcenter(b,[a,c]),[a,c])]),1,2)),['GL02','GL04','GL03','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(a,line([b,c]),1,2)),['GL02','GL04','GL03','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(a,altitude(b,[a,c]),1,2)),['GL02','GL04','GL03','D20','D9']).
derived_lemma(inc(midpoint([a,b]),homothety(a,median(b,[a,c]),1,2)),['GL02','GL04','GL03','D20','D18']).
derived_lemma(inc(midpoint([a,b]),homothety(a,angle_bis(b,[a,c]),1,2)),['GL02','GL04','GL03','D20','L6']).
derived_lemma(inc(midpoint([a,b]),homothety(a,homothety(c,line_x1,2,1),1,2)),['GL04','D20','GL02','GL03','D21','D85']).
derived_lemma(inc(midpoint([a,b]),homothety(a,homothety(a,line_x3,2,1),1,2)),['GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(midpoint([b,c]),c,midpoint([b,c]),b,-1,1),['GL04','GL03','D21']).
derived_lemma(inc(midpoint([b,c]),homothety(c,line([b,foot(outcenter(b,[a,c]),[a,c])]),1,2)),['GL02','GL04','GL03','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(c,line([a,b]),1,2)),['GL02','GL04','GL03','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(c,altitude(b,[a,c]),1,2)),['GL02','GL04','GL03','D21','D9']).
derived_lemma(inc(midpoint([b,c]),homothety(c,median(b,[a,c]),1,2)),['GL02','GL04','GL03','D21','D18']).
derived_lemma(inc(midpoint([b,c]),homothety(c,angle_bis(b,[a,c]),1,2)),['GL02','GL04','GL03','D21','L6']).
derived_lemma(inc(midpoint([b,c]),homothety(c,homothety(c,line_x1,2,1),1,2)),['GL04','GL02','GL03','D21','D85']).
derived_lemma(inc(midpoint([b,c]),homothety(c,homothety(a,line_x3,2,1),1,2)),['D21','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(midpoint([b,c]),b,midpoint([b,c]),c,-1,1),['GL04','GL03','D21']).
derived_lemma(inc(midpoint([b,c]),homothety(b,line([c,foot(outcenter(c,[a,b]),[a,b])]),1,2)),['GL02','GL04','GL03','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(b,line([a,c]),1,2)),['GL02','GL04','GL03','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(b,altitude(c,[a,b]),1,2)),['GL02','GL04','GL03','D21','D10']).
derived_lemma(inc(midpoint([b,c]),homothety(b,median(c,[a,b]),1,2)),['GL02','GL04','GL03','D21','D19']).
derived_lemma(inc(midpoint([b,c]),homothety(b,angle_bis(c,[a,b]),1,2)),['GL02','GL04','GL03','D21','L7']).
derived_lemma(inc(midpoint([b,c]),homothety(b,homothety(a,line_x2,2,1),1,2)),['GL04','D21','GL02','GL03','D22','D86']).
derived_lemma(inc(midpoint([b,c]),homothety(b,homothety(b,line_x1,2,1),1,2)),['GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(midpoint([a,c]),a,midpoint([a,c]),c,-1,1),['GL04','GL03','D22']).
derived_lemma(inc(midpoint([a,c]),homothety(a,line([c,foot(outcenter(c,[a,b]),[a,b])]),1,2)),['GL02','GL04','GL03','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(a,line([b,c]),1,2)),['GL02','GL04','GL03','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(a,altitude(c,[a,b]),1,2)),['GL02','GL04','GL03','D22','D10']).
derived_lemma(inc(midpoint([a,c]),homothety(a,median(c,[a,b]),1,2)),['GL02','GL04','GL03','D22','D19']).
derived_lemma(inc(midpoint([a,c]),homothety(a,angle_bis(c,[a,b]),1,2)),['GL02','GL04','GL03','D22','L7']).
derived_lemma(inc(midpoint([a,c]),homothety(a,homothety(a,line_x2,2,1),1,2)),['GL04','GL02','GL03','D22','D86']).
derived_lemma(inc(midpoint([a,c]),homothety(a,homothety(b,line_x1,2,1),1,2)),['D22','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(midpoint([a,c]),c,midpoint([a,c]),a,-1,1),['GL04','GL03','D22']).
derived_lemma(inc(midpoint([a,c]),homothety(c,line([a,foot(outcenter(a,[b,c]),[b,c])]),1,2)),['GL02','GL04','GL03','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(c,line([a,b]),1,2)),['GL02','GL04','GL03','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(c,altitude(a,[b,c]),1,2)),['GL02','GL04','GL03','D22','D8']).
derived_lemma(inc(midpoint([a,c]),homothety(c,median(a,[b,c]),1,2)),['GL02','GL04','GL03','D22','D17']).
derived_lemma(inc(midpoint([a,c]),homothety(c,angle_bis(a,[b,c]),1,2)),['GL02','GL04','GL03','D22','L5']).
derived_lemma(inc(midpoint([a,c]),homothety(c,homothety(b,line_x3,2,1),1,2)),['GL04','D22','GL02','GL03','D20','D87']).
derived_lemma(inc(midpoint([a,c]),homothety(c,homothety(c,line_x2,2,1),1,2)),['GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(euler(a,[b,c]),orthocenter([a,b],c),euler(a,[b,c]),a,-1,1),['GL04','GL03','D28']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),line([a,foot(outcenter(a,[b,c]),[b,c])]),1,2)),['GL02','GL04','GL03','D28','GD01']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),line([a,c]),1,2)),['GL02','GL04','GL03','D28','GD01']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),line([a,b]),1,2)),['GL02','GL04','GL03','D28','GD01']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),median(a,[b,c]),1,2)),['GL02','GL04','GL03','D28','D17']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),angle_bis(a,[b,c]),1,2)),['GL02','GL04','GL03','D28','L5']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),homothety(b,line_x3,2,1),1,2)),['GL04','D28','GL02','GL03','D20','D87']).
derived_lemma(inc(euler(a,[b,c]),homothety(orthocenter([a,b],c),homothety(c,line_x2,2,1),1,2)),['D28','GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(euler(a,[b,c]),a,euler(a,[b,c]),orthocenter([a,b],c),-1,1),['GL04','GL03','D28']).
derived_lemma(inc(euler(a,[b,c]),homothety(a,altitude(b,[a,c]),1,2)),['GL02','GL04','GL03','D28','D3']).
derived_lemma(inc(euler(a,[b,c]),homothety(a,altitude(c,[a,b]),1,2)),['GL02','GL04','GL03','D28','L3']).
derived_lemma(sratio(euler(b,[a,c]),orthocenter([a,b],c),euler(b,[a,c]),b,-1,1),['GL04','GL03','D29']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),line([b,foot(outcenter(b,[a,c]),[a,c])]),1,2)),['GL02','GL04','GL03','D29','GD01']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),line([b,c]),1,2)),['GL02','GL04','GL03','D29','GD01']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),line([a,b]),1,2)),['GL02','GL04','GL03','D29','GD01']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),median(b,[a,c]),1,2)),['GL02','GL04','GL03','D29','D18']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),angle_bis(b,[a,c]),1,2)),['GL02','GL04','GL03','D29','L6']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),homothety(c,line_x1,2,1),1,2)),['GL04','D29','GL02','GL03','D21','D85']).
derived_lemma(inc(euler(b,[a,c]),homothety(orthocenter([a,b],c),homothety(a,line_x3,2,1),1,2)),['D29','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(euler(b,[a,c]),b,euler(b,[a,c]),orthocenter([a,b],c),-1,1),['GL04','GL03','D29']).
derived_lemma(inc(euler(b,[a,c]),homothety(b,altitude(a,[b,c]),1,2)),['GL02','GL04','GL03','D29','D3']).
derived_lemma(inc(euler(b,[a,c]),homothety(b,altitude(c,[a,b]),1,2)),['GL02','GL04','GL03','D29','L3']).
derived_lemma(sratio(euler(c,[a,b]),orthocenter([a,b],c),euler(c,[a,b]),c,-1,1),['GL04','GL03','D30']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),line([c,foot(outcenter(c,[a,b]),[a,b])]),1,2)),['GL02','GL04','GL03','D30','GD01']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),line([a,c]),1,2)),['GL02','GL04','GL03','D30','GD01']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),line([b,c]),1,2)),['GL02','GL04','GL03','D30','GD01']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),median(c,[a,b]),1,2)),['GL02','GL04','GL03','D30','D19']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),angle_bis(c,[a,b]),1,2)),['GL02','GL04','GL03','D30','L7']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),homothety(a,line_x2,2,1),1,2)),['GL04','D30','GL02','GL03','D22','D86']).
derived_lemma(inc(euler(c,[a,b]),homothety(orthocenter([a,b],c),homothety(b,line_x1,2,1),1,2)),['D30','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(euler(c,[a,b]),c,euler(c,[a,b]),orthocenter([a,b],c),-1,1),['GL04','GL03','D30']).
derived_lemma(inc(euler(c,[a,b]),homothety(c,altitude(a,[b,c]),1,2)),['GL02','GL04','GL03','D30','D3']).
derived_lemma(inc(euler(c,[a,b]),homothety(c,altitude(b,[a,c]),1,2)),['GL02','GL04','GL03','D30','D3']).
derived_lemma(sratio(npcenter([a,b],c),circumcenter([a,b],c),npcenter([a,b],c),orthocenter([a,b],c),-1,1),['GL04','GL03','D31']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),altitude(a,[b,c]),1,2)),['GL02','GL04','GL03','D31','D3']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),altitude(b,[a,c]),1,2)),['GL02','GL04','GL03','D31','D3']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),altitude(c,[a,b]),1,2)),['GL02','GL04','GL03','D31','L3']).
derived_lemma(sratio(npcenter([a,b],c),orthocenter([a,b],c),npcenter([a,b],c),circumcenter([a,b],c),-1,1),['GL04','GL03','D31']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,c]),1,2)),['GL02','GL04','GL03','D31','D1']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,c]),1,2)),['GL02','GL04','GL03','D31','D1']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,b]),1,2)),['GL02','GL04','GL03','D31','L1']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,a_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,b_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,c_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,a]),1,2)),['GL02','GL04','GL03','D31','GL01','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,b]),1,2)),['GL02','GL04','GL03','D31','GL01','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,c]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,b_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,c_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,a]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,b]),1,2)),['GL02','GL04','GL03','D31','GL01','D38','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,c]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,a_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,c_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,a]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,b]),1,2)),['GL02','GL04','GL03','D31','GL01','D39','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,c]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,a_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,b_k]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,a]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','L11','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,b]),1,2)),['GL02','GL04','GL03','D31','GL01','D40','L12','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,a_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L11','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,b_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L11','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,c_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L11','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,a_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L12','D38','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,b_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L12','D39','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,c_k]),1,2)),['GL02','GL04','GL03','D31','GL01','L12','D40','D26']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,a]),1,2)),['GL02','GL04','GL03','D31','GL01','L12','L11','D26']).
derived_lemma(sratio(centroid([a,b],c),circumcenter([a,b],c),centroid([a,b],c),npcenter([a,b],c),-2,1),['GL04','GL03','L15']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L15','GL01','L19','L20','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L15','GL01','L19','L21','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L15','GL01','L20','L19','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L15','GL01','L20','L21','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L15','GL01','L21','L19','D32']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L15','GL01','L21','L20','D32']).
derived_lemma(sratio(centroid([a,b],c),npcenter([a,b],c),centroid([a,b],c),circumcenter([a,b],c),-1,2),['GL04','GL03','L15']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b,c]),1,3)),['GL02','GL04','GL03','L15','D1']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a,c]),1,3)),['GL02','GL04','GL03','L15','D1']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a,b]),1,3)),['GL02','GL04','GL03','L15','L1']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c,a_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c,b_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c,c_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c,a]),1,3)),['GL02','GL04','GL03','L15','GL01','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c,b]),1,3)),['GL02','GL04','GL03','L15','GL01','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,c]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,b_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,c_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,a]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a_k,b]),1,3)),['GL02','GL04','GL03','L15','GL01','D38','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,c]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,a_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,c_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,a]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b_k,b]),1,3)),['GL02','GL04','GL03','L15','GL01','D39','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,c]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,a_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,b_k]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,a]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([c_k,b]),1,3)),['GL02','GL04','GL03','L15','GL01','D40','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a,a_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L11','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a,b_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L11','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([a,c_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L11','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b,a_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L12','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b,b_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L12','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b,c_k]),1,3)),['GL02','GL04','GL03','L15','GL01','L12','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(npcenter([a,b],c),side_bis([b,a]),1,3)),['GL02','GL04','GL03','L15','GL01','L12','L11','D26']).
derived_lemma(sratio(npcenter([a,b],c),centroid([a,b],c),npcenter([a,b],c),orthocenter([a,b],c),-1,3),['GL04','GL03','L16']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),altitude(a,[b,c]),1,4)),['GL02','GL04','GL03','L16','D3']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),altitude(b,[a,c]),1,4)),['GL02','GL04','GL03','L16','D3']).
derived_lemma(inc(npcenter([a,b],c),homothety(centroid([a,b],c),altitude(c,[a,b]),1,4)),['GL02','GL04','GL03','L16','L3']).
derived_lemma(sratio(npcenter([a,b],c),orthocenter([a,b],c),npcenter([a,b],c),centroid([a,b],c),-3,1),['GL04','GL03','L16']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),median(a,[b,c]),3,4)),['GL02','GL04','GL03','L16','D4']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),median(b,[a,c]),3,4)),['GL02','GL04','GL03','L16','D4']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),median(c,[a,b]),3,4)),['GL02','GL04','GL03','L16','L4']).
derived_lemma(sratio(centroid([a,b],c),midpoint([b,c]),centroid([a,b],c),a,-1,2),['GL04','GL03','L55']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),1,3)),['GL02','GL04','GL03','L55','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),line([a,c]),1,3)),['GL02','GL04','GL03','L55','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),line([a,b]),1,3)),['GL02','GL04','GL03','L55','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),altitude(a,[b,c]),1,3)),['GL02','GL04','GL03','L55','D8']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),angle_bis(a,[b,c]),1,3)),['GL02','GL04','GL03','L55','L5']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),homothety(b,line_x3,2,1),1,3)),['GL04','L55','GL02','GL03','D20','D87']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([b,c]),homothety(c,line_x2,2,1),1,3)),['L55','GL02','GL03','GL04','D22','D86']).
derived_lemma(sratio(centroid([a,b],c),a,centroid([a,b],c),midpoint([b,c]),-2,1),['GL04','GL03','L55']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([b,c]),2,3)),['GL02','GL04','GL03','L55','D11']).
derived_lemma(inc(centroid([a,b],c),homothety(a,line_x1,2,3)),['GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),homothety(a,line_x1,2,3),-3,1)),['L16','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),homothety(a,line_x1,2,3),3,2)),['L15','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(a,homothety(midpoint([b,c]),homothety(a,line_x1,2,3),3,1)),['GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(b,homothety(midpoint([a,c]),homothety(a,line_x1,2,3),3,1)),['L56','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(c,homothety(midpoint([a,b]),homothety(a,line_x1,2,3),3,1)),['L57','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),homothety(a,line_x1,2,3),3,1)),['L58','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),homothety(a,line_x1,2,3),3,1)),['L15','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(midpoint([b,c]),homothety(a,homothety(a,line_x1,2,3),3,2)),['GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(midpoint([a,c]),homothety(b,homothety(a,line_x1,2,3),3,2)),['L56','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(midpoint([a,b]),homothety(c,homothety(a,line_x1,2,3),3,2)),['L57','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(a,line_x1,2,3),3,2)),['L58','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(a,line_x1,2,3),3,4)),['L16','GL02','GL04','GL03','L55','D85']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([b,foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L55','GL01','L38','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([b,foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L55','GL01','L39','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([c,b]),2,3)),['GL02','GL04','GL03','L55','GL01','L37','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([c,foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L55','GL01','L37','L38','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([c,foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L55','GL01','L37','L39','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(b,[a,c]),b]),2,3)),['GL02','GL04','GL03','L55','GL01','L38','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(b,[a,c]),c]),2,3)),['GL02','GL04','GL03','L55','GL01','L38','L37','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L55','GL01','L38','L39','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(c,[a,b]),b]),2,3)),['GL02','GL04','GL03','L55','GL01','L39','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(c,[a,b]),c]),2,3)),['GL02','GL04','GL03','L55','GL01','L39','L37','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(a,side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L55','GL01','L39','L38','GD02']).
derived_lemma(sratio(centroid([a,b],c),midpoint([a,c]),centroid([a,b],c),b,-1,2),['GL04','GL03','L56']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),1,3)),['GL02','GL04','GL03','L56','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),line([b,c]),1,3)),['GL02','GL04','GL03','L56','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),line([a,b]),1,3)),['GL02','GL04','GL03','L56','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),altitude(b,[a,c]),1,3)),['GL02','GL04','GL03','L56','D9']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),angle_bis(b,[a,c]),1,3)),['GL02','GL04','GL03','L56','L6']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),homothety(c,line_x1,2,1),1,3)),['GL04','L56','GL02','GL03','D21','D85']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,c]),homothety(a,line_x3,2,1),1,3)),['L56','GL02','GL03','GL04','D20','D87']).
derived_lemma(sratio(centroid([a,b],c),b,centroid([a,b],c),midpoint([a,c]),-2,1),['GL04','GL03','L56']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([a,c]),2,3)),['GL02','GL04','GL03','L56','D12']).
derived_lemma(inc(centroid([a,b],c),homothety(b,line_x2,2,3)),['GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),homothety(b,line_x2,2,3),-3,1)),['L16','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),homothety(b,line_x2,2,3),3,2)),['L15','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(a,homothety(midpoint([b,c]),homothety(b,line_x2,2,3),3,1)),['L55','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(b,homothety(midpoint([a,c]),homothety(b,line_x2,2,3),3,1)),['GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(c,homothety(midpoint([a,b]),homothety(b,line_x2,2,3),3,1)),['L57','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),homothety(b,line_x2,2,3),3,1)),['L58','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),homothety(b,line_x2,2,3),3,1)),['L15','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(midpoint([b,c]),homothety(a,homothety(b,line_x2,2,3),3,2)),['L55','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(midpoint([a,c]),homothety(b,homothety(b,line_x2,2,3),3,2)),['GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(midpoint([a,b]),homothety(c,homothety(b,line_x2,2,3),3,2)),['L57','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(b,line_x2,2,3),3,2)),['L58','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(b,line_x2,2,3),3,4)),['L16','GL02','GL04','GL03','L56','D86']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([c,a]),2,3)),['GL02','GL04','GL03','L56','GL01','L43','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([c,foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L56','GL01','L44','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([c,foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L56','GL01','L45','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([a,foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L56','GL01','L43','L44','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([a,foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L56','GL01','L43','L45','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(a,[b,c]),c]),2,3)),['GL02','GL04','GL03','L56','GL01','L44','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(a,[b,c]),a]),2,3)),['GL02','GL04','GL03','L56','GL01','L44','L43','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,3)),['GL02','GL04','GL03','L56','GL01','L44','L45','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(c,[a,b]),c]),2,3)),['GL02','GL04','GL03','L56','GL01','L45','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(c,[a,b]),a]),2,3)),['GL02','GL04','GL03','L56','GL01','L45','L43','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(b,side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L56','GL01','L45','L44','GD02']).
derived_lemma(sratio(centroid([a,b],c),midpoint([a,b]),centroid([a,b],c),c,-1,2),['GL04','GL03','L57']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),1,3)),['GL02','GL04','GL03','L57','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),line([a,c]),1,3)),['GL02','GL04','GL03','L57','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),line([b,c]),1,3)),['GL02','GL04','GL03','L57','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),altitude(c,[a,b]),1,3)),['GL02','GL04','GL03','L57','D10']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),angle_bis(c,[a,b]),1,3)),['GL02','GL04','GL03','L57','L7']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),homothety(a,line_x2,2,1),1,3)),['GL04','L57','GL02','GL03','D22','D86']).
derived_lemma(inc(centroid([a,b],c),homothety(midpoint([a,b]),homothety(b,line_x1,2,1),1,3)),['L57','GL02','GL03','GL04','D21','D85']).
derived_lemma(sratio(centroid([a,b],c),c,centroid([a,b],c),midpoint([a,b]),-2,1),['GL04','GL03','L57']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([a,b]),2,3)),['GL02','GL04','GL03','L57','D13']).
derived_lemma(inc(centroid([a,b],c),homothety(c,line_x3,2,3)),['GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(orthocenter([a,b],c),homothety(npcenter([a,b],c),homothety(c,line_x3,2,3),-3,1)),['L16','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(npcenter([a,b],c),homothety(circumcenter([a,b],c),homothety(c,line_x3,2,3),3,2)),['L15','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(a,homothety(midpoint([b,c]),homothety(c,line_x3,2,3),3,1)),['L55','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(b,homothety(midpoint([a,c]),homothety(c,line_x3,2,3),3,1)),['L56','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(c,homothety(midpoint([a,b]),homothety(c,line_x3,2,3),3,1)),['GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(orthocenter([a,b],c),homothety(circumcenter([a,b],c),homothety(c,line_x3,2,3),3,1)),['L58','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(circumcenter([a,b],c),homothety(npcenter([a,b],c),homothety(c,line_x3,2,3),3,1)),['L15','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(midpoint([b,c]),homothety(a,homothety(c,line_x3,2,3),3,2)),['L55','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(midpoint([a,c]),homothety(b,homothety(c,line_x3,2,3),3,2)),['L56','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(midpoint([a,b]),homothety(c,homothety(c,line_x3,2,3),3,2)),['GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(circumcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(c,line_x3,2,3),3,2)),['L58','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(npcenter([a,b],c),homothety(orthocenter([a,b],c),homothety(c,line_x3,2,3),3,4)),['L16','GL02','GL04','GL03','L57','D87']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([a,foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L41','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([a,foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L42','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([b,a]),2,3)),['GL02','GL04','GL03','L57','GL01','L40','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([b,foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L40','L41','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([b,foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L40','L42','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(b,[a,c]),a]),2,3)),['GL02','GL04','GL03','L57','GL01','L41','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(b,[a,c]),b]),2,3)),['GL02','GL04','GL03','L57','GL01','L41','L40','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L41','L42','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(a,[b,c]),a]),2,3)),['GL02','GL04','GL03','L57','GL01','L42','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(a,[b,c]),b]),2,3)),['GL02','GL04','GL03','L57','GL01','L42','L40','GD02']).
derived_lemma(inc(centroid([a,b],c),homothety(c,side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,3)),['GL02','GL04','GL03','L57','GL01','L42','L41','GD02']).
derived_lemma(sratio(centroid([a,b],c),circumcenter([a,b],c),centroid([a,b],c),orthocenter([a,b],c),-1,2),['GL04','GL03','L58']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),altitude(a,[b,c]),1,3)),['GL02','GL04','GL03','L58','D3']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),altitude(b,[a,c]),1,3)),['GL02','GL04','GL03','L58','D3']).
derived_lemma(inc(centroid([a,b],c),homothety(circumcenter([a,b],c),altitude(c,[a,b]),1,3)),['GL02','GL04','GL03','L58','L3']).
derived_lemma(sratio(centroid([a,b],c),orthocenter([a,b],c),centroid([a,b],c),circumcenter([a,b],c),-2,1),['GL04','GL03','L58']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,c]),2,3)),['GL02','GL04','GL03','L58','D1']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,c]),2,3)),['GL02','GL04','GL03','L58','D1']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,b]),2,3)),['GL02','GL04','GL03','L58','L1']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,a_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,b_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,c_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,a]),2,3)),['GL02','GL04','GL03','L58','GL01','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c,b]),2,3)),['GL02','GL04','GL03','L58','GL01','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,c]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,b_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,c_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,a]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a_k,b]),2,3)),['GL02','GL04','GL03','L58','GL01','D38','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,c]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,a_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,c_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,a]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b_k,b]),2,3)),['GL02','GL04','GL03','L58','GL01','D39','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,c]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,a_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,b_k]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,a]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','L11','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([c_k,b]),2,3)),['GL02','GL04','GL03','L58','GL01','D40','L12','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,a_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L11','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,b_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L11','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([a,c_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L11','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,a_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L12','D38','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,b_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L12','D39','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,c_k]),2,3)),['GL02','GL04','GL03','L58','GL01','L12','D40','D26']).
derived_lemma(inc(centroid([a,b],c),homothety(orthocenter([a,b],c),side_bis([b,a]),2,3)),['GL02','GL04','GL03','L58','GL01','L12','L11','D26']).
derived_lemma(sratio(midpoint([b,c]),foot(outcenter(a,[b,c]),[b,c]),midpoint([b,c]),foot(incenter([a,b],c),[b,c]),-1,1),['GL04','GL03','L62']).
derived_lemma(inc(midpoint([b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),line_x1,2,1),1,2)),['GL04','GL02','GL03','L62','D85']).
derived_lemma(sratio(midpoint([b,c]),foot(incenter([a,b],c),[b,c]),midpoint([b,c]),foot(outcenter(a,[b,c]),[b,c]),-1,1),['GL04','GL03','L62']).
derived_lemma(inc(midpoint([b,c]),homothety(foot(incenter([a,b],c),[b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),1,2)),['GL02','GL04','GL03','L62','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(foot(incenter([a,b],c),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),line_x1,2,1),1,2)),['GL02','GL03','GL04','L62','D85']).
derived_lemma(sratio(midpoint([a,c]),foot(outcenter(b,[a,c]),[a,c]),midpoint([a,c]),foot(incenter([a,b],c),[a,c]),-1,1),['GL04','GL03','L63']).
derived_lemma(inc(midpoint([a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),line_x2,2,1),1,2)),['GL04','GL02','GL03','L63','D86']).
derived_lemma(sratio(midpoint([a,c]),foot(incenter([a,b],c),[a,c]),midpoint([a,c]),foot(outcenter(b,[a,c]),[a,c]),-1,1),['GL04','GL03','L63']).
derived_lemma(inc(midpoint([a,c]),homothety(foot(incenter([a,b],c),[a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),1,2)),['GL02','GL04','GL03','L63','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(foot(incenter([a,b],c),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),line_x2,2,1),1,2)),['GL02','GL03','GL04','L63','D86']).
derived_lemma(sratio(midpoint([a,b]),foot(outcenter(c,[a,b]),[a,b]),midpoint([a,b]),foot(incenter([a,b],c),[a,b]),-1,1),['GL04','GL03','L64']).
derived_lemma(inc(midpoint([a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),line_x3,2,1),1,2)),['GL04','GL02','GL03','L64','D87']).
derived_lemma(sratio(midpoint([a,b]),foot(incenter([a,b],c),[a,b]),midpoint([a,b]),foot(outcenter(c,[a,b]),[a,b]),-1,1),['GL04','GL03','L64']).
derived_lemma(inc(midpoint([a,b]),homothety(foot(incenter([a,b],c),[a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),1,2)),['GL02','GL04','GL03','L64','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(foot(incenter([a,b],c),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),line_x3,2,1),1,2)),['GL02','GL03','GL04','L64','D87']).
derived_lemma(harm(c,b,angle_bis_out_foot(a,[b,c]),angle_bis_foot(a,[b,c])),['GL05','L77']).
derived_lemma(harm(c,a,angle_bis_out_foot(b,[a,c]),angle_bis_foot(b,[a,c])),['GL05','L78']).
derived_lemma(harm(b,a,angle_bis_out_foot(c,[a,b]),angle_bis_foot(c,[a,b])),['GL05','L79']).
derived_lemma(harm(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c]),b,c),['GL06','L77']).
derived_lemma(harm(angle_bis_out_foot(a,[b,c]),angle_bis_foot(a,[b,c]),c,b),['GL05','GL06','L77']).
derived_lemma(harm(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c]),a,c),['GL06','L78']).
derived_lemma(harm(angle_bis_out_foot(b,[a,c]),angle_bis_foot(b,[a,c]),c,a),['GL05','GL06','L78']).
derived_lemma(harm(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b]),a,b),['GL06','L79']).
derived_lemma(harm(angle_bis_out_foot(c,[a,b]),angle_bis_foot(c,[a,b]),b,a),['GL05','GL06','L79']).
derived_lemma(parallel(side_bis([a,foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL08','D20','D28','L41','L47','L56','L43','GD02','GL02','L58','GL01','L11','D26']).
derived_lemma(parallel(side_bis([a,foot(b,[a,c])]),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL08','D20','D28','L41','L47','D21','L37','L38','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([a,foot(b,[a,c])]),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL08','D20','D28','L41','L47','D21','L38','L37','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([a,foot(b,[a,c])]),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL08','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),a]),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL08','D20','D28','L41','L47','L56','L43','GD02','GL02','L58','GL01','L11','D26']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),a]),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL08','D20','D28','L41','L47','D21','L37','L38','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),a]),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL08','D20','D28','L41','L47','D21','L38','L37','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),a]),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL08','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([a,c])]),homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL08','D20','GL04','D22','GD01','L56','L43','L44','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([a,c])]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL08','D20','GL04','D22','GD01','L56','L44','L43','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([a,c])]),homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL08','GD01','GL04','D20','L42','GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([a,c])]),homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL08','GD01','GL04','D20','L42','GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(parallel(side_bis([a,foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL08','D20','GL04','D22','L56','L44','L43','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([a,foot(a,[b,c])]),homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL08','GL04','D20','L42','GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),a]),homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL08','D20','GL04','D22','L56','L43','L44','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),a]),homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL08','GL04','D20','L42','GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(parallel(side_bis([b,foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL08','D21','D29','L39','L51','L57','L40','GD02','GL02','L58','GL01','L12','L11','D26']).
derived_lemma(parallel(side_bis([b,foot(c,[a,b])]),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL08','D21','D29','L39','L51','D22','L43','L45','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([b,foot(c,[a,b])]),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL08','D21','D29','L39','L51','D22','L45','L43','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([b,foot(c,[a,b])]),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL08','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),b]),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL08','D21','D29','L39','L51','L57','L40','GD02','GL02','L58','GL01','L12','L11','D26']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),b]),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL08','D21','D29','L39','L51','D22','L43','L45','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),b]),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL08','D21','D29','L39','L51','D22','L45','L43','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),b]),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL08','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([b,c])]),homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL08','D21','GL04','D20','GD01','L57','L40','L41','GL02','L55','GL01','L38','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([b,c])]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL08','D21','GL04','D20','GD01','L57','L41','L40','GL02','L55','GL01','L38','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([b,c])]),homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL08','GD01','GL04','D21','L38','GL02','GL03','D20','GL01','L40','L41','GD02']).
derived_lemma(parallel(line([midpoint([a,b]),midpoint([b,c])]),homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL08','GD01','GL04','D21','L38','GL02','GL03','D20','GL01','L41','L40','GD02']).
derived_lemma(parallel(side_bis([b,foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL08','D21','GL04','D20','L57','L41','L40','GL02','L55','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([b,foot(b,[a,c])]),homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL08','GL04','D21','L38','GL02','GL03','D20','GL01','L41','L40','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),b]),homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL08','D21','GL04','D20','L57','L40','L41','GL02','L55','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),b]),homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL08','GL04','D21','L38','GL02','GL03','D20','GL01','L40','L41','GD02']).
derived_lemma(parallel(side_bis([c,foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL08','D22','D30','L44','L54','L55','L37','GD02','GL02','L58','GL01','L12','D26']).
derived_lemma(parallel(side_bis([c,foot(a,[b,c])]),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL08','D22','D30','L44','L54','D20','L40','L42','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([c,foot(a,[b,c])]),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL08','D22','D30','L44','L54','D20','L42','L40','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([c,foot(a,[b,c])]),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL08','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),c]),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL08','D22','D30','L44','L54','L55','L37','GD02','GL02','L58','GL01','L12','D26']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),c]),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL08','D22','D30','L44','L54','D20','L40','L42','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),c]),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL08','D22','D30','L44','L54','D20','L42','L40','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),c]),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL08','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(parallel(line([midpoint([a,c]),midpoint([b,c])]),homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL08','D22','GL04','D21','GD01','L55','L37','L39','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(line([midpoint([a,c]),midpoint([b,c])]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL08','D22','GL04','D21','GD01','L55','L39','L37','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(line([midpoint([a,c]),midpoint([b,c])]),homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL08','GD01','GL04','D22','L45','GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(parallel(line([midpoint([a,c]),midpoint([b,c])]),homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL08','GD01','GL04','D22','L45','GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(parallel(side_bis([c,foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL08','D22','GL04','D21','L55','L39','L37','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([c,foot(c,[a,b])]),homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL08','GL04','D22','L45','GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),c]),homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL08','D22','GL04','D21','L55','L37','L39','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),c]),homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL08','GL04','D22','L45','GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(parallel(side_bis([a,foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL08','D28','GL04','D22','L48','L43','L45','L58','L12','L11','D26','GL02','L57','GL01','L40','GD02']).
derived_lemma(parallel(side_bis([a,foot(c,[a,b])]),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL08','GL04','D28','L48','GL02','GL03','D22','GL01','L45','L43','GD02']).
derived_lemma(parallel(side_bis([a,foot(c,[a,b])]),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL08','D28','D22','L48','L43','L45','D29','L51','GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(parallel(side_bis([a,foot(c,[a,b])]),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL08','D28','D22','L48','L43','L45','D29','L51','GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),a]),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL08','D28','GL04','D22','L48','L45','L43','L58','L12','L11','D26','GL02','L57','GL01','L40','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),a]),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL08','GL04','D28','L48','GL02','GL03','D22','GL01','L43','L45','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),a]),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL08','D28','D22','L48','L45','L43','D29','L51','GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),a]),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL08','D28','D22','L48','L45','L43','D29','L51','GL02','GL03','GL04','D21','GL01','L39','GD02']).
derived_lemma(parallel(side_bis([b,foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL08','D29','GL04','D20','L50','L40','L42','L58','L12','D26','GL02','L55','GL01','L37','GD02']).
derived_lemma(parallel(side_bis([b,foot(a,[b,c])]),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL08','GL04','D29','L50','GL02','GL03','D20','GL01','L42','L40','GD02']).
derived_lemma(parallel(side_bis([b,foot(a,[b,c])]),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL08','D29','D20','L50','L40','L42','D30','L54','GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(parallel(side_bis([b,foot(a,[b,c])]),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL08','D29','D20','L50','L40','L42','D30','L54','GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),b]),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL08','D29','GL04','D20','L50','L42','L40','L58','L12','D26','GL02','L55','GL01','L37','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),b]),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL08','GL04','D29','L50','GL02','GL03','D20','GL01','L40','L42','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),b]),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL08','D29','D20','L50','L42','L40','D30','L54','GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),b]),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL08','D29','D20','L50','L42','L40','D30','L54','GL02','GL03','GL04','D22','GL01','L44','GD02']).
derived_lemma(parallel(side_bis([c,foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL08','D30','GL04','D21','L53','L37','L38','L58','L11','D26','GL02','L56','GL01','L43','GD02']).
derived_lemma(parallel(side_bis([c,foot(b,[a,c])]),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL08','D30','D21','L53','L37','L38','D28','L47','GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(parallel(side_bis([c,foot(b,[a,c])]),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL08','D30','D21','L53','L37','L38','D28','L47','GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(parallel(side_bis([c,foot(b,[a,c])]),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL08','GL04','D30','L53','GL02','GL03','D21','GL01','L38','L37','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),c]),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL08','D30','GL04','D21','L53','L38','L37','L58','L11','D26','GL02','L56','GL01','L43','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),c]),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL08','D30','D21','L53','L38','L37','D28','L47','GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),c]),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL08','D30','D21','L53','L38','L37','D28','L47','GL02','GL03','GL04','D20','GL01','L41','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),c]),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL08','GL04','D30','L53','GL02','GL03','D21','GL01','L37','L38','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(c,[a,b])]),line([a,circumcenter([a,b],c)])),['GL08','D31','GL04','D28','L20','L21','D32','GL01','L47','L48','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(c,[a,b])]),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),2,1)),['GL08','GL04','D31','L21','L20','D32','GL02','GL03','D28','GL01','L48','L47','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(b,[a,c])]),-2,1)),['GL08','D31','D28','L47','L48','GL04','L15','L21','L20','D32','GL02','L55','GL01','L39','L38','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(b,[a,c])]),line([a,circumcenter([a,b],c)])),['GL08','D31','GL04','D28','L21','L20','D32','GL01','L48','L47','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(b,[a,c])]),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),2,1)),['GL08','GL04','D31','L20','L21','D32','GL02','GL03','D28','GL01','L47','L48','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(c,[a,b])]),-2,1)),['GL08','D31','D28','L48','L47','GL04','L15','L20','L21','D32','GL02','L55','GL01','L38','L39','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(c,[a,b])]),line([b,circumcenter([a,b],c)])),['GL08','D31','GL04','D29','L19','L21','D32','GL01','L50','L51','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(c,[a,b])]),homothety(orthocenter([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),2,1)),['GL08','GL04','D31','L21','L19','D32','GL02','GL03','D29','GL01','L51','L50','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),foot(a,[b,c])]),-2,1)),['GL08','D31','D29','L50','L51','GL04','L15','L21','L19','D32','GL02','L56','GL01','L45','L44','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(a,[b,c])]),line([b,circumcenter([a,b],c)])),['GL08','D31','GL04','D29','L21','L19','D32','GL01','L51','L50','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(a,[b,c])]),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),2,1)),['GL08','GL04','D31','L19','L21','D32','GL02','GL03','D29','GL01','L50','L51','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(c,[a,b])]),-2,1)),['GL08','D31','D29','L51','L50','GL04','L15','L19','L21','D32','GL02','L56','GL01','L44','L45','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(b,[a,c])]),line([c,circumcenter([a,b],c)])),['GL08','D31','GL04','D30','L19','L20','D32','GL01','L54','L53','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(b,[a,c])]),homothety(orthocenter([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),2,1)),['GL08','GL04','D31','L20','L19','D32','GL02','GL03','D30','GL01','L53','L54','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),foot(a,[b,c])]),-2,1)),['GL08','D31','D30','L54','L53','GL04','L15','L20','L19','D32','GL02','L57','GL01','L41','L42','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(a,[b,c])]),line([c,circumcenter([a,b],c)])),['GL08','D31','GL04','D30','L20','L19','D32','GL01','L53','L54','GD02','GD01']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(a,[b,c])]),homothety(orthocenter([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),2,1)),['GL08','GL04','D31','L19','L20','D32','GL02','GL03','D30','GL01','L54','L53','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),foot(b,[a,c])]),-2,1)),['GL08','D31','D30','L53','L54','GL04','L15','L19','L20','D32','GL02','L57','GL01','L42','L41','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL08','D28','GL04','D29','L46','L48','L49','L51','L55','L37','L39','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(c,[a,b])]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL08','D28','GL04','D29','L46','L48','L49','L51','L55','L39','L37','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(c,[a,b])]),homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL08','D28','D29','L46','L48','L49','L51','GL04','D22','L45','GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(c,[a,b])]),homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL08','D28','D29','L46','L48','L49','L51','GL04','D22','L45','GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL08','D28','GL04','D29','L48','L46','L51','L49','L55','L37','L39','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL08','D28','GL04','D29','L48','L46','L51','L49','L55','L39','L37','GL02','L56','GL01','L45','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),orthocenter([a,b],c)]),homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL08','D28','D29','L48','L46','L51','L49','GL04','D22','L45','GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(parallel(side_bis([foot(c,[a,b]),orthocenter([a,b],c)]),homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL08','D28','D29','L48','L46','L51','L49','GL04','D22','L45','GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL08','D28','GL04','D30','L46','L47','L52','L53','L55','L38','GL02','L57','GL01','L40','L41','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(b,[a,c])]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL08','D28','GL04','D30','L46','L47','L52','L53','L55','L38','GL02','L57','GL01','L41','L40','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(b,[a,c])]),homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL08','D28','D30','L46','L47','L52','L53','D20','L40','L41','GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(b,[a,c])]),homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL08','D28','D30','L46','L47','L52','L53','D20','L41','L40','GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL08','D28','GL04','D30','L47','L46','L53','L52','L55','L38','GL02','L57','GL01','L40','L41','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL08','D28','GL04','D30','L47','L46','L53','L52','L55','L38','GL02','L57','GL01','L41','L40','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),orthocenter([a,b],c)]),homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL08','D28','D30','L47','L46','L53','L52','D20','L40','L41','GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([foot(b,[a,c]),orthocenter([a,b],c)]),homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL08','D28','D30','L47','L46','L53','L52','D20','L41','L40','GL02','GL03','GL04','D21','GL01','L38','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL08','D29','GL04','D30','L49','L50','L52','L54','L56','L43','L44','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(a,[b,c])]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL08','D29','GL04','D30','L49','L50','L52','L54','L56','L44','L43','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(a,[b,c])]),homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL08','D29','D30','L49','L50','L52','L54','GL04','D20','L42','GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(parallel(side_bis([orthocenter([a,b],c),foot(a,[b,c])]),homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL08','D29','D30','L49','L50','L52','L54','GL04','D20','L42','GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL08','D29','GL04','D30','L50','L49','L54','L52','L56','L43','L44','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),orthocenter([a,b],c)]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL08','D29','GL04','D30','L50','L49','L54','L52','L56','L44','L43','GL02','L57','GL01','L42','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),orthocenter([a,b],c)]),homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL08','D29','D30','L50','L49','L54','L52','GL04','D20','L42','GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(parallel(side_bis([foot(a,[b,c]),orthocenter([a,b],c)]),homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL08','D29','D30','L50','L49','L54','L52','GL04','D20','L42','GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(parallel(side_bis([c,b]),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL08','L55','L58','L37','L12','D26','D20','L40','L42','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([c,b]),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL08','L55','L58','L37','L12','D26','D20','L42','L40','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(parallel(side_bis([c,b]),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL08','L55','L58','L37','L12','D26','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(parallel(side_bis([c,b]),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL08','L55','L58','L37','L12','D26','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(parallel(side_bis([c,a]),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL08','L56','L58','L43','L11','D26','D21','L37','L38','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([c,a]),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL08','L56','L58','L43','L11','D26','D21','L38','L37','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(parallel(side_bis([c,a]),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL08','L56','L58','L43','L11','D26','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(parallel(side_bis([c,a]),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL08','L56','L58','L43','L11','D26','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(parallel(side_bis([b,a]),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL08','L57','L58','L40','L12','L11','D26','D22','L43','L45','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([b,a]),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL08','L57','L58','L40','L12','L11','D26','D22','L45','L43','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(parallel(side_bis([b,a]),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL08','L57','L58','L40','L12','L11','D26','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(parallel(side_bis([b,a]),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL08','L57','L58','L40','L12','L11','D26','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(inc(midpoint([a,b]),line([a,b])),['GL09','D20','GD01']).
derived_lemma(inc(c,homothety(centroid([a,b],c),line([a,b]),-2,1)),['GL02','L57','GL09','D20','GD01']).
derived_lemma(inc(foot(incenter([a,b],c),[a,b]),homothety(foot(outcenter(c,[a,b]),[a,b]),line([a,b]),2,1)),['GL02','GL03','L64','GL09','D20','GD01']).
derived_lemma(inc(foot(outcenter(c,[a,b]),[a,b]),homothety(foot(incenter([a,b],c),[a,b]),line([a,b]),2,1)),['GL02','GL03','GL04','L64','GL09','D20','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(c,line([a,b]),2,3)),['GL02','GL04','GL03','L57','GL09','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(midpoint([a,b]),line([a,b]),-1,1)),['GL09','GL02','GL04','D20','GD01']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),side_bis([c,foot(c,[a,b])]),-2,1)),['GL09','D20','L55','L37','L39','GL02','L56','GL01','L45','GD02']).
derived_lemma(inc(midpoint([a,b]),homothety(centroid([a,b],c),side_bis([foot(c,[a,b]),c]),-2,1)),['GL09','D20','L55','L39','L37','GL02','L56','GL01','L45','GD02']).
derived_lemma(inc(midpoint([a,b]),homothety(c,side_bis([c,foot(c,[a,b])]),2,1)),['GL09','D20','GL04','D22','L45','GL02','GL03','D21','GL01','L37','L39','GD02']).
derived_lemma(inc(midpoint([a,b]),homothety(c,side_bis([foot(c,[a,b]),c]),2,1)),['GL09','D20','GL04','D22','L45','GL02','GL03','D21','GL01','L39','L37','GD02']).
derived_lemma(inc(midpoint([b,c]),line([b,c])),['GL09','D21','GD01']).
derived_lemma(inc(a,homothety(centroid([a,b],c),line([b,c]),-2,1)),['GL02','L55','GL09','D21','GD01']).
derived_lemma(inc(foot(incenter([a,b],c),[b,c]),homothety(foot(outcenter(a,[b,c]),[b,c]),line([b,c]),2,1)),['GL02','GL03','L62','GL09','D21','GD01']).
derived_lemma(inc(foot(outcenter(a,[b,c]),[b,c]),homothety(foot(incenter([a,b],c),[b,c]),line([b,c]),2,1)),['GL02','GL03','GL04','L62','GL09','D21','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(a,line([b,c]),2,3)),['GL02','GL04','GL03','L55','GL09','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(midpoint([b,c]),line([b,c]),-1,1)),['GL09','GL02','GL04','D21','GD01']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),side_bis([a,foot(a,[b,c])]),-2,1)),['GL09','D21','L56','L43','L44','GL02','L57','GL01','L42','GD02']).
derived_lemma(inc(midpoint([b,c]),homothety(centroid([a,b],c),side_bis([foot(a,[b,c]),a]),-2,1)),['GL09','D21','L56','L44','L43','GL02','L57','GL01','L42','GD02']).
derived_lemma(inc(midpoint([b,c]),homothety(a,side_bis([a,foot(a,[b,c])]),2,1)),['GL09','D21','GL04','D20','L42','GL02','GL03','D22','GL01','L43','L44','GD02']).
derived_lemma(inc(midpoint([b,c]),homothety(a,side_bis([foot(a,[b,c]),a]),2,1)),['GL09','D21','GL04','D20','L42','GL02','GL03','D22','GL01','L44','L43','GD02']).
derived_lemma(inc(midpoint([a,c]),line([a,c])),['GL09','D22','GD01']).
derived_lemma(inc(b,homothety(centroid([a,b],c),line([a,c]),-2,1)),['GL02','L56','GL09','D22','GD01']).
derived_lemma(inc(foot(incenter([a,b],c),[a,c]),homothety(foot(outcenter(b,[a,c]),[a,c]),line([a,c]),2,1)),['GL02','GL03','L63','GL09','D22','GD01']).
derived_lemma(inc(foot(outcenter(b,[a,c]),[a,c]),homothety(foot(incenter([a,b],c),[a,c]),line([a,c]),2,1)),['GL02','GL03','GL04','L63','GL09','D22','GD01']).
derived_lemma(inc(centroid([a,b],c),homothety(b,line([a,c]),2,3)),['GL02','GL04','GL03','L56','GL09','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(midpoint([a,c]),line([a,c]),-1,1)),['GL09','GL02','GL04','D22','GD01']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),side_bis([b,foot(b,[a,c])]),-2,1)),['GL09','D22','L57','L40','L41','GL02','L55','GL01','L38','GD02']).
derived_lemma(inc(midpoint([a,c]),homothety(centroid([a,b],c),side_bis([foot(b,[a,c]),b]),-2,1)),['GL09','D22','L57','L41','L40','GL02','L55','GL01','L38','GD02']).
derived_lemma(inc(midpoint([a,c]),homothety(b,side_bis([b,foot(b,[a,c])]),2,1)),['GL09','D22','GL04','D21','L38','GL02','GL03','D20','GL01','L40','L41','GD02']).
derived_lemma(inc(midpoint([a,c]),homothety(b,side_bis([foot(b,[a,c]),b]),2,1)),['GL09','D22','GL04','D21','L38','GL02','GL03','D20','GL01','L41','L40','GD02']).
derived_lemma(inc(euler(a,[b,c]),altitude(a,[b,c])),['GL09','D28','D8','D3']).
derived_lemma(inc(euler(a,[b,c]),homothety(euler(a,[b,c]),altitude(a,[b,c]),-1,1)),['GL09','D3','GL02','GL04','D28','D8']).
derived_lemma(inc(euler(a,[b,c]),homothety(centroid([a,b],c),side_bis([b,c]),-2,1)),['GL09','D28','L55','D11','GL02','L58','D1']).
derived_lemma(inc(euler(a,[b,c]),homothety(centroid([a,b],c),side_bis([c,b]),-2,1)),['GL09','D28','L55','L37','GD02','GL02','L58','GL01','L12','D26']).
derived_lemma(inc(euler(a,[b,c]),homothety(b,side_bis([b,foot(a,[b,c])]),2,1)),['GL09','D28','D20','L40','L42','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(inc(euler(a,[b,c]),homothety(b,side_bis([foot(a,[b,c]),b]),2,1)),['GL09','D28','D20','L42','L40','GL02','GL03','GL04','D29','GL01','L50','GD02']).
derived_lemma(inc(euler(a,[b,c]),homothety(c,side_bis([c,foot(a,[b,c])]),2,1)),['GL09','D28','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(inc(euler(a,[b,c]),homothety(c,side_bis([foot(a,[b,c]),c]),2,1)),['GL09','D28','D22','L44','GL02','GL03','GL04','D30','GL01','L54','GD02']).
derived_lemma(inc(euler(b,[a,c]),altitude(b,[a,c])),['GL09','D29','D9','D3']).
derived_lemma(inc(euler(b,[a,c]),homothety(euler(b,[a,c]),altitude(b,[a,c]),-1,1)),['GL09','D3','GL02','GL04','D29','D9']).
derived_lemma(inc(euler(b,[a,c]),homothety(centroid([a,b],c),side_bis([a,c]),-2,1)),['GL09','D29','L56','D12','GL02','L58','D1']).
derived_lemma(inc(euler(b,[a,c]),homothety(centroid([a,b],c),side_bis([c,a]),-2,1)),['GL09','D29','L56','L43','GD02','GL02','L58','GL01','L11','D26']).
derived_lemma(inc(euler(b,[a,c]),homothety(c,side_bis([c,foot(b,[a,c])]),2,1)),['GL09','D29','D21','L37','L38','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(inc(euler(b,[a,c]),homothety(c,side_bis([foot(b,[a,c]),c]),2,1)),['GL09','D29','D21','L38','L37','GL02','GL03','GL04','D30','GL01','L53','GD02']).
derived_lemma(inc(euler(b,[a,c]),homothety(a,side_bis([a,foot(b,[a,c])]),2,1)),['GL09','D29','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(inc(euler(b,[a,c]),homothety(a,side_bis([foot(b,[a,c]),a]),2,1)),['GL09','D29','D20','L41','GL02','GL03','GL04','D28','GL01','L47','GD02']).
derived_lemma(inc(euler(c,[a,b]),altitude(c,[a,b])),['GL09','D30','D10','L3']).
derived_lemma(inc(euler(c,[a,b]),homothety(euler(c,[a,b]),altitude(c,[a,b]),-1,1)),['GL09','L3','GL02','GL04','D30','D10']).
derived_lemma(inc(euler(c,[a,b]),homothety(centroid([a,b],c),side_bis([a,b]),-2,1)),['GL09','D30','L57','D13','GL02','L58','L1']).
derived_lemma(inc(euler(c,[a,b]),homothety(centroid([a,b],c),side_bis([b,a]),-2,1)),['GL09','D30','L57','L40','GD02','GL02','L58','GL01','L12','L11','D26']).
derived_lemma(inc(euler(c,[a,b]),homothety(a,side_bis([a,foot(c,[a,b])]),2,1)),['GL09','D30','D22','L43','L45','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(inc(euler(c,[a,b]),homothety(a,side_bis([foot(c,[a,b]),a]),2,1)),['GL09','D30','D22','L45','L43','GL02','GL03','GL04','D28','GL01','L48','GD02']).
derived_lemma(inc(euler(c,[a,b]),homothety(b,side_bis([b,foot(c,[a,b])]),2,1)),['GL09','D30','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(inc(euler(c,[a,b]),homothety(b,side_bis([foot(c,[a,b]),b]),2,1)),['GL09','D30','D21','L39','GL02','GL03','GL04','D29','GL01','L51','GD02']).
derived_lemma(perp_line_to_circ(line([a,b]),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['GL10','L8']).
derived_lemma(perp_line_to_circ(line([a,b]),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['GL10','L9']).
derived_lemma(perp_line_to_circ(line([a,c]),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['GL10','L10']).
derived_lemma(perp_line_to_circ(line([a,c]),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['GL11','L8']).
derived_lemma(perp_line_to_circ(line([b,c]),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['GL11','L9']).
derived_lemma(perp_line_to_circ(line([b,c]),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['GL11','L10']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,0,0,0),['GL12','L98','L99']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,0),['GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),angle(line([a,b]),angle_bis(a,[b,c])),1,0,1,1),['GL12','L98','L110']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,0),['GL12','L98','L122']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,0),['GL12','L99','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),angle(angle_bis(a,[b,c]),line([a,c])),1,0,1,1),['GL12','L99','L110']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,0),['GL12','L99','L122']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),1,0,0,0),['GL12','L100','L101']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,0),['GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),angle(line([b,c]),angle_bis(b,[a,c])),1,0,1,1),['GL12','L100','L111']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,0),['GL12','L100','L120']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,0),['GL12','L101','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,0,1,1),['GL12','L101','L111']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,0),['GL12','L101','L120']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),1,0,0,0),['GL12','L102','L103']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,0),['GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),angle(line([a,c]),angle_bis(c,[a,b])),1,0,1,1),['GL12','L102','L112']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,0),['GL12','L102','L121']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,0),['GL12','L103','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),angle(angle_bis(c,[a,b]),line([b,c])),1,0,1,1),['GL12','L103','L112']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,0),['GL12','L103','L121']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,1,0,0),['GL12','L107','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,1,0,0),['GL12','L107','L99']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,1,1,1),['GL12','L107','L110']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,0,0,0),['GL12','L107','L122']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,1,0,0),['GL12','L108','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,1,0,0),['GL12','L108','L101']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,1,1,1),['GL12','L108','L111']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,0,0,0),['GL12','L108','L120']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,1,0,0),['GL12','L109','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,1,0,0),['GL12','L109','L103']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,1,1,1),['GL12','L109','L112']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,0,0,0),['GL12','L109','L121']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,1,0,0),['GL12','L120','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,1,0,0),['GL12','L120','L101']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,0,0,0),['GL12','L120','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,1,1,1),['GL12','L120','L111']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,1,0,0),['GL12','L121','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,1,0,0),['GL12','L121','L103']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,0,0,0),['GL12','L121','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,1,1,1),['GL12','L121','L112']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,1,0,0),['GL12','L122','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,1,0,0),['GL12','L122','L99']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,0,0,0),['GL12','L122','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,1,1,1),['GL12','L122','L110']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,-1),['GL13','GL12','L98','L107','D14']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,-1),['GL13','GL12','L98','L107','D14']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,0,0,-1),['L122','GL13','GL12','L98','L107','D14']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([a,b]),line([a,c])),1,0,0,-1),['GL13','GL12','L107','L98']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,-1),['GL13','GL12','L98','L122','D14']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,-1),['GL13','GL12','L98','L122','D14']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,0,0,-1),['L107','GL13','GL12','L98','L122','D14']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([a,b]),line([a,c])),1,0,0,-1),['GL13','GL12','L122','L98']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,-1),['GL13','GL12','L100','L108','D15']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,-1),['GL13','GL12','L100','L108','D15']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,0,0,-1),['L120','GL13','GL12','L100','L108','D15']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([b,c]),line([a,b])),1,0,0,-1),['GL13','GL12','L108','L100']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,-1),['GL13','GL12','L100','L120','D15']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,-1),['GL13','GL12','L100','L120','D15']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,0,0,-1),['L108','GL13','GL12','L100','L120','D15']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([b,c]),line([a,b])),1,0,0,-1),['GL13','GL12','L120','L100']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,-1),['GL13','GL12','L102','L109','D16']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,-1),['GL13','GL12','L102','L109','D16']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,0,0,-1),['L121','GL13','GL12','L102','L109','D16']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([a,c]),line([b,c])),1,0,0,-1),['GL13','GL12','L109','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,-1),['GL13','GL12','L102','L121','D16']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,-1),['GL13','GL12','L102','L121','D16']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,0,0,-1),['L109','GL13','GL12','L102','L121','D16']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,c]),line([b,c])),1,0,0,-1),['GL13','GL12','L121','L102']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([a,b]),line([a,c])),1,1,0,1),['GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,0,0,1),['L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,1,0,1),['GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,1,0,1),['L122','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([a,b]),line([a,c])),1,1,0,1),['L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,0,0,1),['L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,1,0,1),['L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,1,0,1),['L122','L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([b,c]),line([a,b])),1,1,0,1),['GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,0,0,1),['L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,1,0,1),['GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,1,0,1),['L120','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([b,c]),line([a,b])),1,1,0,1),['L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),1,0,0,1),['L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,1,0,1),['L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,1,0,1),['L120','L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([a,c]),line([b,c])),1,1,0,1),['GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(angle_bis(c,[a,b]),line([b,c])),1,0,0,1),['L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,1,0,1),['GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,1,0,1),['L121','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,c]),line([b,c])),1,1,0,1),['L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),1,0,0,1),['L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,1,0,1),['L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,1,0,1),['L121','L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,-1),['GL15','L98','D14']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,-1),['GL12','GL15','L98','D14']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,0,0,-1),['L107','GL12','GL15','L98','D14']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,0,0,-1),['L122','GL12','GL15','L98','D14']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,-1,0,0),['GL15','L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),1,-1,0,0),['D14','GL15','L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),1,0,0,0),['D14','GL15','L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),1,0,0,0),['L122','D14','GL15','L99','GL13','GL12','L98','L107']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,-1),['GL15','L100','D15']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,-1),['GL12','GL15','L100','D15']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,0,0,-1),['L108','GL12','GL15','L100','D15']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,0,0,-1),['L120','GL12','GL15','L100','D15']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(angle_bis(b,[a,c]),line([a,b])),1,-1,0,0),['GL15','L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),1,-1,0,0),['D15','GL15','L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),1,0,0,0),['D15','GL15','L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),1,0,0,0),['L120','D15','GL15','L101','GL13','GL12','L100','L108']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,-1),['GL15','L102','D16']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,-1),['GL12','GL15','L102','D16']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,0,0,-1),['L109','GL12','GL15','L102','D16']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,0,0,-1),['L121','GL12','GL15','L102','D16']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(angle_bis(c,[a,b]),line([b,c])),1,-1,0,0),['GL15','L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),1,-1,0,0),['D16','GL15','L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),1,0,0,0),['D16','GL15','L103','GL13','GL12','L102','L109']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),1,0,0,0),['L121','D16','GL15','L103','GL13','GL12','L102','L109']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,circle_center_through(euler(a,[b,c]),a),1,2)),['GL16','D20','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,circle_center_through(point_n(b,[a,c]),a),1,2)),['GL16','D20','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,circle_center_through(midpoint([a,c]),c),1,2)),['GL16','D20','L43']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),1,2)),['GL16','D20','L71']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,circle_center_through(euler(b,[a,c]),b),1,2)),['GL16','D21','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,circle_center_through(point_n(c,[a,b]),b),1,2)),['GL16','D21','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,circle_center_through(midpoint([a,b]),a),1,2)),['GL16','D21','L40']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),1,2)),['GL16','D21','L73']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,circle_center_through(euler(c,[a,b]),c),1,2)),['GL16','D22','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,circle_center_through(point_n(a,[b,c]),c),1,2)),['GL16','D22','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,circle_center_through(midpoint([b,c]),b),1,2)),['GL16','D22','L37']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),1,2)),['GL16','D22','L72']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([a,b]),a),1,2)),['GL16','D28','GD02']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(b,[a,c]),a),1,2)),['GL16','D28','GD02']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2)),['GL16','D28','L11']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(c,[a,b]),b),1,2)),['GL16','D28','L35']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([a,c]),c),1,2)),['GL16','D28','L43']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),1,2)),['GL16','D28','L71']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([b,c]),b),1,2)),['GL16','D29','GD02']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(c,[a,b]),b),1,2)),['GL16','D29','GD02']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2)),['GL16','D29','L12']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(a,[b,c]),c),1,2)),['GL16','D29','L31']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([a,b]),a),1,2)),['GL16','D29','L40']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),1,2)),['GL16','D29','L73']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([a,c]),c),1,2)),['GL16','D30','GD02']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(a,[b,c]),c),1,2)),['GL16','D30','GD02']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2)),['GL16','D30','D26']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),circle_center_through(point_n(b,[a,c]),a),1,2)),['GL16','D30','L33']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),circle_center_through(midpoint([b,c]),b),1,2)),['GL16','D30','L37']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),1,2)),['GL16','D30','L72']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(a,[b,c]),a),1,2)),['GL16','D31','L46']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(b,[a,c]),b),1,2)),['GL16','D31','L49']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(c,[a,b]),c),1,2)),['GL16','D31','L52']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(a,[b,c]),a),1,4)),['GL16','L16','L46']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(b,[a,c]),b),1,4)),['GL16','L16','L49']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(c,[a,b]),c),1,4)),['GL16','L16','L52']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circle_center_through(euler(a,[b,c]),a),1,3)),['GL16','L55','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circle_center_through(midpoint([a,b]),a),1,3)),['GL16','L55','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circle_center_through(point_n(b,[a,c]),a),1,3)),['GL16','L55','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3)),['GL16','L55','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circle_center_through(point_n(c,[a,b]),b),1,3)),['GL16','L55','L35']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),circle_center_through(midpoint([a,c]),c),1,3)),['GL16','L55','L43']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),1,3)),['GL16','L55','L71']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circle_center_through(euler(b,[a,c]),b),1,3)),['GL16','L56','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circle_center_through(midpoint([b,c]),b),1,3)),['GL16','L56','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circle_center_through(point_n(c,[a,b]),b),1,3)),['GL16','L56','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3)),['GL16','L56','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circle_center_through(point_n(a,[b,c]),c),1,3)),['GL16','L56','L31']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),circle_center_through(midpoint([a,b]),a),1,3)),['GL16','L56','L40']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),1,3)),['GL16','L56','L73']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circle_center_through(euler(c,[a,b]),c),1,3)),['GL16','L57','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circle_center_through(midpoint([a,c]),c),1,3)),['GL16','L57','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circle_center_through(point_n(a,[b,c]),c),1,3)),['GL16','L57','GD02']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3)),['GL16','L57','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circle_center_through(point_n(b,[a,c]),a),1,3)),['GL16','L57','L33']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),circle_center_through(midpoint([b,c]),b),1,3)),['GL16','L57','L37']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),1,3)),['GL16','L57','L72']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(a,[b,c]),a),1,3)),['GL16','L58','L46']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(b,[a,c]),b),1,3)),['GL16','L58','L49']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),circle_center_through(euler(c,[a,b]),c),1,3)),['GL16','L58','L52']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2)),['GL16','L62','D27']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),diam(incenter([a,b],c),midpoint([b,c])),1,2)),['GL16','L62','L74']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2)),['GL16','L63','L13']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),diam(incenter([a,b],c),midpoint([a,c])),1,2)),['GL16','L63','L75']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2)),['GL16','L64','L14']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),diam(incenter([a,b],c),midpoint([a,b])),1,2)),['GL16','L64','L76']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','D20','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','D20','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','D20','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D20','L11']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,2)),['D21','GL16','GL03','D20','L11']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,2)),['D29','GL16','GL03','D20','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,3)),['L56','GL16','GL03','D20','L11']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','D20','L35']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','D20','L43']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),-1,1)),['GL16','GL03','D20','L71']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','D21','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','D21','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','D21','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D21','L12']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,2)),['D22','GL16','GL03','D21','L12']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,2)),['D30','GL16','GL03','D21','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,3)),['L57','GL16','GL03','D21','L12']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','D21','L31']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','D21','L40']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),-1,1)),['GL16','GL03','D21','L73']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['D21','GL16','GL03','D20','L11']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','D22','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','D22','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','D22','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D22','D26']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,2)),['D20','GL16','GL03','D22','D26']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,2)),['D28','GL16','GL03','D22','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,3)),['L55','GL16','GL03','D22','D26']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['D20','GL16','GL03','D22','D26']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','D22','L33']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','D22','L37']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),-1,1)),['GL16','GL03','D22','L72']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['D22','GL16','GL03','D21','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','D28','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','D28','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','D28','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D28','L11']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,2)),['D31','GL16','GL03','D28','L11']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,4)),['L16','GL16','GL03','D28','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,3)),['L58','GL16','GL03','D28','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','D28','L35']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','D28','L43']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),-1,1)),['GL16','GL03','D28','L71']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['D28','GL16','GL03','D22','D26']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','D29','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','D29','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','D29','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D29','L12']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,2)),['D31','GL16','GL03','D29','L12']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,4)),['L16','GL16','GL03','D29','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,3)),['L58','GL16','GL03','D29','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','D29','L31']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','D29','L40']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),-1,1)),['GL16','GL03','D29','L73']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['D29','GL16','GL03','D20','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','D30','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','D30','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','D30','GD02']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1)),['GL16','GL03','D30','D26']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,2)),['D31','GL16','GL03','D30','D26']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,4)),['L16','GL16','GL03','D30','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,3)),['L58','GL16','GL03','D30','D26']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','D30','L33']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','D30','L37']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),-1,1)),['GL16','GL03','D30','L72']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['D30','GL16','GL03','D21','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','D31','L46']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','D31','L49']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','D31','L52']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,1)),['D31','GL16','GL03','D28','L11']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,1)),['D31','GL16','GL03','D29','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,1)),['D31','GL16','GL03','D30','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(a,[b,c]),a),-1,3)),['GL16','GL03','L16','L46']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(b,[a,c]),b),-1,3)),['GL16','GL03','L16','L49']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),circle_center_through(euler(c,[a,b]),c),-1,3)),['GL16','GL03','L16','L52']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,3)),['L16','GL16','GL03','D28','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,3)),['L16','GL16','GL03','D29','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,3)),['L16','GL16','GL03','D30','D26']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circle_center_through(euler(a,[b,c]),a),-1,2)),['GL16','GL03','L55','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([a,b]),a),-1,2)),['GL16','GL03','L55','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(b,[a,c]),a),-1,2)),['GL16','GL03','L55','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2)),['GL16','GL03','L55','L11']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(c,[a,b]),b),-1,2)),['GL16','GL03','L55','L35']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([a,c]),c),-1,2)),['GL16','GL03','L55','L43']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),-1,2)),['GL16','GL03','L55','L71']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,2)),['L55','GL16','GL03','D22','D26']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circle_center_through(euler(b,[a,c]),b),-1,2)),['GL16','GL03','L56','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([b,c]),b),-1,2)),['GL16','GL03','L56','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(c,[a,b]),b),-1,2)),['GL16','GL03','L56','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2)),['GL16','GL03','L56','L12']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(a,[b,c]),c),-1,2)),['GL16','GL03','L56','L31']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([a,b]),a),-1,2)),['GL16','GL03','L56','L40']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),-1,2)),['GL16','GL03','L56','L73']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,2)),['L56','GL16','GL03','D20','L11']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circle_center_through(euler(c,[a,b]),c),-1,2)),['GL16','GL03','L57','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([a,c]),c),-1,2)),['GL16','GL03','L57','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(a,[b,c]),c),-1,2)),['GL16','GL03','L57','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2)),['GL16','GL03','L57','D26']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circle_center_through(point_n(b,[a,c]),a),-1,2)),['GL16','GL03','L57','L33']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),circle_center_through(midpoint([b,c]),b),-1,2)),['GL16','GL03','L57','L37']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),-1,2)),['GL16','GL03','L57','L72']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,2)),['L57','GL16','GL03','D21','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(a,[b,c]),a),-1,2)),['GL16','GL03','L58','L46']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(b,[a,c]),b),-1,2)),['GL16','GL03','L58','L49']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),circle_center_through(euler(c,[a,b]),c),-1,2)),['GL16','GL03','L58','L52']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,2)),['L58','GL16','GL03','D28','L11']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,2)),['L58','GL16','GL03','D29','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,2)),['L58','GL16','GL03','D30','D26']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(midpoint([b,c]),incircle([a,b],c),-1,1)),['GL16','GL03','L62','D27']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(midpoint([b,c]),diam(incenter([a,b],c),midpoint([b,c])),-1,1)),['GL16','GL03','L62','L74']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(midpoint([a,c]),incircle([a,b],c),-1,1)),['GL16','GL03','L63','L13']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(midpoint([a,c]),diam(incenter([a,b],c),midpoint([a,c])),-1,1)),['GL16','GL03','L63','L75']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(midpoint([a,b]),incircle([a,b],c),-1,1)),['GL16','GL03','L64','L14']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(midpoint([a,b]),diam(incenter([a,b],c),midpoint([a,b])),-1,1)),['GL16','GL03','L64','L76']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,circle_center_through(euler(b,[a,c]),b),1,2)),['GL16','GL04','D20','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,circle_center_through(midpoint([b,c]),b),1,2)),['GL16','GL04','D20','GD02']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,circle_center_through(point_n(a,[b,c]),c),1,2)),['GL16','GL04','D20','L31']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),1,2)),['GL16','GL04','D20','L73']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D20','L11']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','GL04','D20','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','GL04','D20','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','GL04','D20','GD02']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1)),['GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,2)),['D28','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,3)),['L55','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['D28','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,2)),['L55','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','GL04','D20','L31']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','GL04','D20','L40']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c])),-1,1)),['GL16','GL03','GL04','D20','L73']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D20','L11']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,circle_center_through(euler(c,[a,b]),c),1,2)),['GL16','GL04','D21','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,circle_center_through(midpoint([a,c]),c),1,2)),['GL16','GL04','D21','GD02']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,circle_center_through(point_n(b,[a,c]),a),1,2)),['GL16','GL04','D21','L33']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),1,2)),['GL16','GL04','D21','L72']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D21','L12']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','GL04','D21','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','GL04','D21','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circle_center_through(point_n(a,[b,c]),c),-1,1)),['GL16','GL03','GL04','D21','GD02']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,2)),['D29','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,3)),['L56','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['D29','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,2)),['L56','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),1,2)),['D20','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['D20','GL16','GL03','GL04','D21','D26']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','GL04','D21','L33']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),circle_center_through(midpoint([b,c]),b),-1,1)),['GL16','GL03','GL04','D21','L37']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b])),-1,1)),['GL16','GL03','GL04','D21','L72']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D21','L12']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,circle_center_through(euler(a,[b,c]),a),1,2)),['GL16','GL04','D22','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,circle_center_through(midpoint([a,b]),a),1,2)),['GL16','GL04','D22','GD02']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,circle_center_through(point_n(c,[a,b]),b),1,2)),['GL16','GL04','D22','L35']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),1,2)),['GL16','GL04','D22','L71']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D22','D26']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),1,2)),['D22','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','GL04','D22','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circle_center_through(midpoint([a,b]),a),-1,1)),['GL16','GL03','GL04','D22','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circle_center_through(point_n(b,[a,c]),a),-1,1)),['GL16','GL03','GL04','D22','GD02']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1)),['GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,2)),['D30','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,3)),['L57','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['D30','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,2)),['L57','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),1,2)),['D21','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['D21','GL16','GL03','GL04','D22','L11']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circle_center_through(point_n(c,[a,b]),b),-1,1)),['GL16','GL03','GL04','D22','L35']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),circle_center_through(midpoint([a,c]),c),-1,1)),['GL16','GL03','GL04','D22','L43']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c])),-1,1)),['GL16','GL03','GL04','D22','L71']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D22','D26']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),-1,1),-1,1)),['D22','GL16','GL03','GL04','D20','L12']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,circle_center_through(euler(b,[a,c]),b),1,2)),['GL16','GL04','D28','L49']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,circle_center_through(euler(c,[a,b]),c),1,2)),['GL16','GL04','D28','L52']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D28','L11']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D28','GL16','GL03','D29','L12']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D28','GL16','GL03','D30','D26']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','GL04','D28','L46']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','GL04','D28','L49']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','GL04','D28','L52']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D28','L11']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D28','GL16','GL03','D29','L12']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D28','GL16','GL03','D30','D26']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,circle_center_through(euler(a,[b,c]),a),1,2)),['GL16','GL04','D29','L46']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,circle_center_through(euler(c,[a,b]),c),1,2)),['GL16','GL04','D29','L52']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D29','GL16','GL03','D28','L11']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D29','L12']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D29','GL16','GL03','D30','D26']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','GL04','D29','L46']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','GL04','D29','L49']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','GL04','D29','L52']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D29','GL16','GL03','D28','L11']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D29','L12']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D29','GL16','GL03','D30','D26']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,circle_center_through(euler(a,[b,c]),a),1,2)),['GL16','GL04','D30','L46']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,circle_center_through(euler(b,[a,c]),b),1,2)),['GL16','GL04','D30','L49']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D30','GL16','GL03','D28','L11']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),1,2)),['GL04','D30','GL16','GL03','D29','L12']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','D30','D26']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),circle_center_through(euler(a,[b,c]),a),-1,1)),['GL16','GL03','GL04','D30','L46']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),circle_center_through(euler(b,[a,c]),b),-1,1)),['GL16','GL03','GL04','D30','L49']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),circle_center_through(euler(c,[a,b]),c),-1,1)),['GL16','GL03','GL04','D30','L52']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(euler(a,[b,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D30','GL16','GL03','D28','L11']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(euler(b,[a,c]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','D30','GL16','GL03','D29','L12']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(euler(c,[a,b]),circumcircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','D30','D26']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,4)),['GL04','L16','GL16','L55','L11']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,4)),['GL04','L16','GL16','L56','L12']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,4)),['GL04','L16','GL16','L57','D26']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),-3,1)),['GL03','GL04','L16','GL16','L55','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),-3,1)),['GL03','GL04','L16','GL16','L56','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),-3,1)),['GL03','GL04','L16','GL16','L57','D26']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3)),['GL16','GL04','L55','D32']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),3,4)),['L16','GL16','GL04','L55','D32']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),-3,1)),['GL03','L16','GL16','GL04','L55','D32']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(a,homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),2,3)),['GL04','L55','GL16','L62','D27']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(a,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,3)),['GL04','GL16','GL03','L55','L11']).
derived_lemma(inc_k(a,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1)),['GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D20','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D28','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,3)),['GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D20','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D28','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,2)),['GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D22','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D22','GL16','GL03','GL04','L55','D32']).
derived_lemma(inc_k(a,homothety_circ(centroid([a,b],c),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),-2,1)),['GL03','GL04','L55','GL16','L62','D27']).
derived_lemma(inc_k(a,homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),-2,1)),['GL04','GL16','GL03','L55','L11']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3)),['GL16','GL04','L56','L17']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),3,4)),['L16','GL16','GL04','L56','L17']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),-3,1)),['GL03','L16','GL16','GL04','L56','L17']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(b,homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),2,3)),['GL04','L56','GL16','L63','L13']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(b,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,3)),['GL04','GL16','GL03','L56','L12']).
derived_lemma(inc_k(b,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1)),['GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D21','GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D29','GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,3)),['GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D21','GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D29','GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,2)),['GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D20','GL16','GL03','GL04','L56','L17']).
derived_lemma(inc_k(b,homothety_circ(centroid([a,b],c),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),-2,1)),['GL03','GL04','L56','GL16','L63','L13']).
derived_lemma(inc_k(b,homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),-2,1)),['GL04','GL16','GL03','L56','L12']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3)),['GL16','GL04','L57','L18']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),3,4)),['L16','GL16','GL04','L57','L18']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),-3,1)),['GL03','L16','GL16','GL04','L57','L18']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(c,homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),2,3)),['GL04','L57','GL16','L64','L14']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(c,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,3)),['GL04','GL16','GL03','L57','D26']).
derived_lemma(inc_k(c,homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1)),['GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,2)),['D30','GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),1,3)),['GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D22','GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D30','GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,2)),['GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(centroid([a,b],c),npcircle([a,b],c),-2,1),-1,1)),['D21','GL16','GL03','GL04','L57','L18']).
derived_lemma(inc_k(c,homothety_circ(centroid([a,b],c),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),-2,1)),['GL03','GL04','L57','GL16','L64','L14']).
derived_lemma(inc_k(c,homothety_circ(centroid([a,b],c),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),-2,1)),['GL04','GL16','GL03','L57','D26']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),homothety_circ(midpoint([b,c]),incircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','L62','D27']).
derived_lemma(inc_k(foot(incenter([a,b],c),[b,c]),homothety_circ(midpoint([b,c]),homothety_circ(midpoint([b,c]),incircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','L62','D27']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),homothety_circ(midpoint([a,c]),incircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','L63','L13']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,c]),homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,c]),incircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','L63','L13']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),homothety_circ(midpoint([a,b]),incircle([a,b],c),-1,1),1,2)),['GL04','GL16','GL03','L64','L14']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,b]),homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,b]),incircle([a,b],c),-1,1),-1,1)),['GL04','GL16','GL03','L64','L14']).
derived_lemma(inc_k(b,homothety_circ(a,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['D21','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['D29','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(a,npcircle([a,b],c),2,1),1,3)),['L56','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D21','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D29','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),-1,2)),['L56','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(b,homothety_circ(a,homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D20','GL16','L64','L14']).
derived_lemma(inc_k(b,homothety_circ(a,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D20','GL16','GL03','L57','D26']).
derived_lemma(inc_k(a,homothety_circ(b,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['D28','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(b,npcircle([a,b],c),2,1),1,3)),['L55','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D28','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),-1,2)),['L55','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['D22','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D22','GL16','GL04','GL03','D20','L18']).
derived_lemma(inc_k(a,homothety_circ(b,homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D20','GL16','L64','L14']).
derived_lemma(inc_k(a,homothety_circ(b,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D20','GL16','GL03','L57','D26']).
derived_lemma(inc_k(c,homothety_circ(b,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['D30','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(b,npcircle([a,b],c),2,1),1,3)),['L57','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D22','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D30','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),-1,2)),['L57','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(b,homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(c,homothety_circ(b,homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D21','GL16','L62','D27']).
derived_lemma(inc_k(c,homothety_circ(b,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D21','GL16','GL03','L55','L11']).
derived_lemma(inc_k(b,homothety_circ(c,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['D29','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(c,npcircle([a,b],c),2,1),1,3)),['L56','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D29','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),-1,2)),['L56','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(a,homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['D20','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D20','GL16','GL04','GL03','D21','D32']).
derived_lemma(inc_k(b,homothety_circ(c,homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D21','GL16','L62','D27']).
derived_lemma(inc_k(b,homothety_circ(c,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D21','GL16','GL03','L55','L11']).
derived_lemma(inc_k(a,homothety_circ(c,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['D28','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(c,npcircle([a,b],c),2,1),1,3)),['L55','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D20','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D28','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),-1,2)),['L55','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(a,homothety_circ(c,homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D22','GL16','L63','L13']).
derived_lemma(inc_k(a,homothety_circ(c,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D22','GL16','GL03','L56','L12']).
derived_lemma(inc_k(c,homothety_circ(a,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(a,homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['D30','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(a,npcircle([a,b],c),2,1),1,3)),['L57','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D30','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),-1,2)),['L57','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D21','GL16','GL04','GL03','D22','L17']).
derived_lemma(inc_k(c,homothety_circ(a,homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','D22','GL16','L63','L13']).
derived_lemma(inc_k(c,homothety_circ(a,homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','D22','GL16','GL03','L56','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['D31','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),1,4)),['L16','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),1,3)),['L58','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D31','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),-1,3)),['L16','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(a,npcircle([a,b],c),2,1),-1,2)),['L58','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(a,homothety_circ(a,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D29','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(a,npcircle([a,b],c),2,1),-1,1)),['D30','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(a,homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D28','L11']).
derived_lemma(inc_k(a,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(b,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['D20','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([b,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,3)),['L55','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,b]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D20','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(a,[b,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(centroid([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,2)),['L55','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(c,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['D22','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D22','GL16','GL04','GL03','D28','L22']).
derived_lemma(inc_k(a,homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D28','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['D31','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),1,4)),['L16','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),1,3)),['L58','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D31','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),-1,3)),['L16','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(b,npcircle([a,b],c),2,1),-1,2)),['L58','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D28','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(b,homothety_circ(b,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(b,npcircle([a,b],c),2,1),-1,1)),['D30','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(b,homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D29','L12']).
derived_lemma(inc_k(b,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(c,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['D21','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,3)),['L56','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(c,homothety_circ(midpoint([b,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D21','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(b,[a,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(centroid([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,2)),['L56','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,b]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D20','GL16','GL04','GL03','D29','L23']).
derived_lemma(inc_k(b,homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D29','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['D31','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),1,4)),['L16','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),1,3)),['L58','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D31','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),-1,3)),['L16','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(centroid([a,b],c),homothety_circ(c,npcircle([a,b],c),2,1),-1,2)),['L58','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(a,homothety_circ(euler(a,[b,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D28','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(b,homothety_circ(euler(b,[a,c]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['D29','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(c,homothety_circ(c,npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(c,homothety_circ(euler(c,[a,b]),homothety_circ(c,npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(c,homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D30','D26']).
derived_lemma(inc_k(c,homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(centroid([a,b],c),homothety_circ(midpoint([a,b]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),1,3)),['L57','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(a,homothety_circ(midpoint([a,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D22','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(euler(c,[a,b]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(centroid([a,b],c),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,2)),['L57','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(b,homothety_circ(midpoint([b,c]),homothety_circ(orthocenter([a,b],c),npcircle([a,b],c),2,1),-1,1)),['D21','GL16','GL04','GL03','D30','L24']).
derived_lemma(inc_k(c,homothety_circ(orthocenter([a,b],c),homothety_circ(orthocenter([a,b],c),circumcircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','D30','D26']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L15','GL16','L55','L11']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L15','GL16','L56','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L15','GL16','L57','D26']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),3,1)),['GL03','L15','GL16','GL04','L55','D32']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),3,1)),['GL03','L15','GL16','GL04','L56','L17']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(npcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),3,1)),['GL03','L15','GL16','GL04','L57','L18']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L15','GL16','L55','L11']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L15','GL16','L56','L12']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L15','GL16','L57','D26']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),3,2)),['GL03','L15','GL16','GL04','L55','D32']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),3,2)),['GL03','L15','GL16','GL04','L56','L17']).
derived_lemma(inc_k(npcenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),3,2)),['GL03','L15','GL16','GL04','L57','L18']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','GL16','L55','L11']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L55','GL16','L56','L12']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L55','GL16','L57','D26']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(a,npcircle([a,b],c),2,3),3,2)),['GL03','GL16','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(b,npcircle([a,b],c),2,3),3,2)),['GL03','L55','GL16','GL04','L56','L17']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(a,homothety_circ(c,npcircle([a,b],c),2,3),3,2)),['GL03','L55','GL16','GL04','L57','L18']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','GL16','L55','L11']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L55','GL16','L56','L12']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L55','GL16','L57','D26']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(a,npcircle([a,b],c),2,3),3,1)),['GL03','GL16','GL04','L55','D32']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(b,npcircle([a,b],c),2,3),3,1)),['GL03','L55','GL16','GL04','L56','L17']).
derived_lemma(inc_k(a,homothety_circ(midpoint([b,c]),homothety_circ(c,npcircle([a,b],c),2,3),3,1)),['GL03','L55','GL16','GL04','L57','L18']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L56','GL16','L55','L11']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','GL16','L56','L12']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L56','GL16','L57','D26']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(a,npcircle([a,b],c),2,3),3,2)),['GL03','L56','GL16','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(b,npcircle([a,b],c),2,3),3,2)),['GL03','GL16','GL04','L56','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(b,homothety_circ(c,npcircle([a,b],c),2,3),3,2)),['GL03','L56','GL16','GL04','L57','L18']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L56','GL16','L55','L11']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','GL16','L56','L12']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L56','GL16','L57','D26']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(a,npcircle([a,b],c),2,3),3,1)),['GL03','L56','GL16','GL04','L55','D32']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(b,npcircle([a,b],c),2,3),3,1)),['GL03','GL16','GL04','L56','L17']).
derived_lemma(inc_k(b,homothety_circ(midpoint([a,c]),homothety_circ(c,npcircle([a,b],c),2,3),3,1)),['GL03','L56','GL16','GL04','L57','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L57','GL16','L55','L11']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L57','GL16','L56','L12']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','GL16','L57','D26']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(a,npcircle([a,b],c),2,3),3,2)),['GL03','L57','GL16','GL04','L55','D32']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(b,npcircle([a,b],c),2,3),3,2)),['GL03','L57','GL16','GL04','L56','L17']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(c,homothety_circ(c,npcircle([a,b],c),2,3),3,2)),['GL03','GL16','GL04','L57','L18']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L57','GL16','L55','L11']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L57','GL16','L56','L12']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','GL16','L57','D26']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(a,npcircle([a,b],c),2,3),3,1)),['GL03','L57','GL16','GL04','L55','D32']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(b,npcircle([a,b],c),2,3),3,1)),['GL03','L57','GL16','GL04','L56','L17']).
derived_lemma(inc_k(c,homothety_circ(midpoint([a,b]),homothety_circ(c,npcircle([a,b],c),2,3),3,1)),['GL03','GL16','GL04','L57','L18']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L58','GL16','L55','L11']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L58','GL16','L56','L12']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,2)),['GL04','GL03','L58','GL16','L57','D26']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),3,2)),['GL03','L58','GL16','GL04','L55','D32']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),3,2)),['GL03','L58','GL16','GL04','L56','L17']).
derived_lemma(inc_k(circumcenter([a,b],c),homothety_circ(orthocenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),3,2)),['GL03','L58','GL16','GL04','L57','L18']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([b,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L58','GL16','L55','L11']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([a,c]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L58','GL16','L56','L12']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(midpoint([a,b]),circumcircle([a,b],c),1,3),3,1)),['GL04','GL03','L58','GL16','L57','D26']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(a,npcircle([a,b],c),2,3),3,1)),['GL03','L58','GL16','GL04','L55','D32']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(b,npcircle([a,b],c),2,3),3,1)),['GL03','L58','GL16','GL04','L56','L17']).
derived_lemma(inc_k(orthocenter([a,b],c),homothety_circ(circumcenter([a,b],c),homothety_circ(c,npcircle([a,b],c),2,3),3,1)),['GL03','L58','GL16','GL04','L57','L18']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(foot(incenter([a,b],c),[b,c]),homothety_circ(midpoint([b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L62','D27']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(foot(incenter([a,b],c),[b,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L62','GL16','GL03','L55','L11']).
derived_lemma(inc_k(foot(incenter([a,b],c),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(midpoint([b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(midpoint([b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L62','D32']).
derived_lemma(inc_k(foot(incenter([a,b],c),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L62','D27']).
derived_lemma(inc_k(foot(incenter([a,b],c),[b,c]),homothety_circ(foot(outcenter(a,[b,c]),[b,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L62','GL16','GL03','L55','L11']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,c]),homothety_circ(midpoint([a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L63','L13']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(foot(incenter([a,b],c),[a,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L63','GL16','GL03','L56','L12']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(midpoint([a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(midpoint([a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L63','L17']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L63','L13']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,c]),homothety_circ(foot(outcenter(b,[a,c]),[a,c]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L63','GL16','GL03','L56','L12']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,b]),homothety_circ(midpoint([a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L64','L14']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(foot(incenter([a,b],c),[a,b]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L64','GL16','GL03','L57','D26']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),npcircle([a,b],c),2,1)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(midpoint([a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),npcircle([a,b],c),2,1),1,2)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(midpoint([a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),npcircle([a,b],c),2,1),-1,1)),['GL16','GL04','GL03','L64','L18']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),incircle([a,b],c),1,2),2,1)),['GL04','GL03','GL16','L64','L14']).
derived_lemma(inc_k(foot(incenter([a,b],c),[a,b]),homothety_circ(foot(outcenter(c,[a,b]),[a,b]),homothety_circ(centroid([a,b],c),circumcircle([a,b],c),-1,2),2,1)),['GL04','L64','GL16','GL03','L57','D26']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,circumcenter([a,b],c)])),angle(altitude(a,[b,c]),angle_bis(a,[b,c])),1,0,0,0),['GL17','L104']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([b,circumcenter([a,b],c)])),angle(altitude(b,[a,c]),angle_bis(b,[a,c])),1,0,0,0),['GL17','L105']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([c,circumcenter([a,b],c)])),angle(altitude(c,[a,b]),angle_bis(c,[a,b])),1,0,0,0),['GL17','L106']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),2,0,0,0),['GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(angle_bis(a,[b,c]),line([a,c])),2,0,0,0),['GL12','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),2,1,0,0),['GL12','L107','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),2,1,0,0),['GL12','L122','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(angle_bis(a,[b,c]),line([a,c])),2,1,0,1),['GL13','GL12','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),2,2,0,1),['L107','GL13','GL12','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),2,2,0,1),['L122','GL13','GL12','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(line([a,b]),line([a,c])),2,2,0,1),['GL15','L107','GL13','GL12','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([a,b]),angle_bis(a,[b,c])),2,1,0,1),['GL13','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),2,2,0,1),['GL12','L107','GL13','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),2,2,0,1),['GL12','L122','GL13','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(line([a,b]),line([a,c])),2,2,0,1),['D14','GL15','GL12','L107','GL13','L99','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([a,b]),angle_bis(a,[b,c])),2,0,0,0),['GL13','L107','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(angle_bis(a,[b,c]),line([a,c])),2,0,0,0),['GL12','L99','GL13','L107','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),2,1,0,0),['GL12','L122','GL13','L107','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([a,b]),line([a,c])),2,1,0,0),['GL15','GL12','L99','GL13','L107','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([a,b]),angle_bis(a,[b,c])),2,0,0,0),['GL13','L122','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(angle_bis(a,[b,c]),line([a,c])),2,0,0,0),['GL12','L99','GL13','L122','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),2,1,0,0),['GL12','L107','GL13','L122','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(line([a,b]),line([a,c])),2,1,0,0),['GL15','L107','GL12','L99','GL13','L122','GL18','L98']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),2,0,0,0),['GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(angle_bis(b,[a,c]),line([a,b])),2,0,0,0),['GL12','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),2,1,0,0),['GL12','L108','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),2,1,0,0),['GL12','L120','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(angle_bis(b,[a,c]),line([a,b])),2,1,0,1),['GL13','GL12','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),2,2,0,1),['L108','GL13','GL12','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),2,2,0,1),['L120','GL13','GL12','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(line([b,c]),line([a,b])),2,2,0,1),['GL15','L108','GL13','GL12','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([b,c]),angle_bis(b,[a,c])),2,1,0,1),['GL13','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),2,2,0,1),['GL12','L108','GL13','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),2,2,0,1),['GL12','L120','GL13','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(line([b,c]),line([a,b])),2,2,0,1),['D15','GL15','GL12','L108','GL13','L101','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([b,c]),angle_bis(b,[a,c])),2,0,0,0),['GL13','L108','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(angle_bis(b,[a,c]),line([a,b])),2,0,0,0),['GL12','L101','GL13','L108','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),2,1,0,0),['GL12','L120','GL13','L108','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([b,c]),line([a,b])),2,1,0,0),['GL15','GL12','L101','GL13','L108','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([b,c]),angle_bis(b,[a,c])),2,0,0,0),['GL13','L120','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(angle_bis(b,[a,c]),line([a,b])),2,0,0,0),['GL12','L101','GL13','L120','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),2,1,0,0),['GL12','L108','GL13','L120','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(line([b,c]),line([a,b])),2,1,0,0),['GL15','L108','GL12','L101','GL13','L120','GL18','L100']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),2,0,0,0),['GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(angle_bis(c,[a,b]),line([b,c])),2,0,0,0),['GL12','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),2,1,0,0),['GL12','L109','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),2,1,0,0),['GL12','L121','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(angle_bis(c,[a,b]),line([b,c])),2,1,0,1),['GL13','GL12','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),2,2,0,1),['L109','GL13','GL12','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),2,2,0,1),['L121','GL13','GL12','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(line([a,c]),line([b,c])),2,2,0,1),['GL15','L109','GL13','GL12','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,c]),angle_bis(c,[a,b])),2,1,0,1),['GL13','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),2,2,0,1),['GL12','L109','GL13','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),2,2,0,1),['GL12','L121','GL13','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(line([a,c]),line([b,c])),2,2,0,1),['D16','GL15','GL12','L109','GL13','L103','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([a,c]),angle_bis(c,[a,b])),2,0,0,0),['GL13','L109','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(angle_bis(c,[a,b]),line([b,c])),2,0,0,0),['GL12','L103','GL13','L109','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),2,1,0,0),['GL12','L121','GL13','L109','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([a,c]),line([b,c])),2,1,0,0),['GL15','GL12','L103','GL13','L109','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,c]),angle_bis(c,[a,b])),2,0,0,0),['GL13','L121','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(angle_bis(c,[a,b]),line([b,c])),2,0,0,0),['GL12','L103','GL13','L121','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),2,1,0,0),['GL12','L109','GL13','L121','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(line([a,c]),line([b,c])),2,1,0,0),['GL15','L109','GL12','L103','GL13','L121','GL18','L102']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(line([foot(a,[b,c]),foot(b,[a,c])]),altitude(a,[b,c])),2,0,0,0),['GL18','L113']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(line([foot(b,[a,c]),foot(c,[a,b])]),altitude(b,[a,c])),2,0,0,0),['GL18','L114']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(line([foot(c,[a,b]),foot(a,[b,c])]),altitude(c,[a,b])),2,0,0,0),['GL18','L115']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([a,c])),angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),2,0,-1,0),['GL20','L110']).
derived_lemma(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),2,1,-1,1),['GL13','L98','GL20','L110']).
derived_lemma(eq_angle_compound(angle(angle_bis(a,[b,c]),line([a,c])),angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),2,1,-1,1),['GL13','L99','GL20','L110']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),2,0,-1,0),['GL13','L107','GL20','L110']).
derived_lemma(eq_angle_compound(angle(line([foot(c,[a,b]),foot(a,[b,c])]),line([b,c])),angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])),2,0,-1,0),['GL13','L122','GL20','L110']).
derived_lemma(eq_angle_compound(angle(line([b,c]),line([a,b])),angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),2,0,-1,0),['GL20','L111']).
derived_lemma(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),2,1,-1,1),['GL13','L100','GL20','L111']).
derived_lemma(eq_angle_compound(angle(angle_bis(b,[a,c]),line([a,b])),angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),2,1,-1,1),['GL13','L101','GL20','L111']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),2,0,-1,0),['GL13','L108','GL20','L111']).
derived_lemma(eq_angle_compound(angle(line([foot(a,[b,c]),foot(b,[a,c])]),line([a,c])),angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])),2,0,-1,0),['GL13','L120','GL20','L111']).
derived_lemma(eq_angle_compound(angle(line([a,c]),line([b,c])),angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),2,0,-1,0),['GL20','L112']).
derived_lemma(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),2,1,-1,1),['GL13','L102','GL20','L112']).
derived_lemma(eq_angle_compound(angle(angle_bis(c,[a,b]),line([b,c])),angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),2,1,-1,1),['GL13','L103','GL20','L112']).
derived_lemma(eq_angle_compound(angle(line([a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),2,0,-1,0),['GL13','L109','GL20','L112']).
derived_lemma(eq_angle_compound(angle(line([foot(b,[a,c]),foot(c,[a,b])]),line([a,b])),angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])),2,0,-1,0),['GL13','L121','GL20','L112']).
