:- discontiguous def_inst/2.
:- discontiguous def/3.

def_inst(inc(c,line([c,circumcenter([a,b],c)])),['GD01']).
def_inst(inc(circumcenter([a,b],c),line([c,circumcenter([a,b],c)])),['GD01']).
def(line([c,circumcenter([a,b],c)]),[inc(c,line([c,circumcenter([a,b],c)])),inc(circumcenter([a,b],c),line([c,circumcenter([a,b],c)]))],'GD01').
def_inst(inc(b,line([b,circumcenter([a,b],c)])),['GD01']).
def_inst(inc(circumcenter([a,b],c),line([b,circumcenter([a,b],c)])),['GD01']).
def(line([b,circumcenter([a,b],c)]),[inc(b,line([b,circumcenter([a,b],c)])),inc(circumcenter([a,b],c),line([b,circumcenter([a,b],c)]))],'GD01').
def_inst(inc(a,line([a,circumcenter([a,b],c)])),['GD01']).
def_inst(inc(circumcenter([a,b],c),line([a,circumcenter([a,b],c)])),['GD01']).
def(line([a,circumcenter([a,b],c)]),[inc(a,line([a,circumcenter([a,b],c)])),inc(circumcenter([a,b],c),line([a,circumcenter([a,b],c)]))],'GD01').
def_inst(inc(foot(c,[a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),['GD01']).
def_inst(inc(foot(a,[b,c]),line([foot(c,[a,b]),foot(a,[b,c])])),['GD01']).
def(line([foot(c,[a,b]),foot(a,[b,c])]),[inc(foot(c,[a,b]),line([foot(c,[a,b]),foot(a,[b,c])])),inc(foot(a,[b,c]),line([foot(c,[a,b]),foot(a,[b,c])]))],'GD01').
def_inst(inc(foot(b,[a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),['GD01']).
def_inst(inc(foot(c,[a,b]),line([foot(b,[a,c]),foot(c,[a,b])])),['GD01']).
def(line([foot(b,[a,c]),foot(c,[a,b])]),[inc(foot(b,[a,c]),line([foot(b,[a,c]),foot(c,[a,b])])),inc(foot(c,[a,b]),line([foot(b,[a,c]),foot(c,[a,b])]))],'GD01').
def_inst(inc(foot(a,[b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),['GD01']).
def_inst(inc(foot(b,[a,c]),line([foot(a,[b,c]),foot(b,[a,c])])),['GD01']).
def(line([foot(a,[b,c]),foot(b,[a,c])]),[inc(foot(a,[b,c]),line([foot(a,[b,c]),foot(b,[a,c])])),inc(foot(b,[a,c]),line([foot(a,[b,c]),foot(b,[a,c])]))],'GD01').
def_inst(inc(midpoint([a,c]),line([midpoint([a,c]),midpoint([b,c])])),['GD01']).
def_inst(inc(midpoint([b,c]),line([midpoint([a,c]),midpoint([b,c])])),['GD01']).
def(line([midpoint([a,c]),midpoint([b,c])]),[inc(midpoint([a,c]),line([midpoint([a,c]),midpoint([b,c])])),inc(midpoint([b,c]),line([midpoint([a,c]),midpoint([b,c])]))],'GD01').
def_inst(inc(midpoint([a,b]),line([midpoint([a,b]),midpoint([b,c])])),['GD01']).
def_inst(inc(midpoint([b,c]),line([midpoint([a,b]),midpoint([b,c])])),['GD01']).
def(line([midpoint([a,b]),midpoint([b,c])]),[inc(midpoint([a,b]),line([midpoint([a,b]),midpoint([b,c])])),inc(midpoint([b,c]),line([midpoint([a,b]),midpoint([b,c])]))],'GD01').
def_inst(inc(midpoint([a,b]),line([midpoint([a,b]),midpoint([a,c])])),['GD01']).
def_inst(inc(midpoint([a,c]),line([midpoint([a,b]),midpoint([a,c])])),['GD01']).
def(line([midpoint([a,b]),midpoint([a,c])]),[inc(midpoint([a,b]),line([midpoint([a,b]),midpoint([a,c])])),inc(midpoint([a,c]),line([midpoint([a,b]),midpoint([a,c])]))],'GD01').
def_inst(inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([a,b])])),['GD01']).
def_inst(inc(midpoint([a,b]),line([incenter([a,b],c),midpoint([a,b])])),['GD01']).
def(line([incenter([a,b],c),midpoint([a,b])]),[inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([a,b])])),inc(midpoint([a,b]),line([incenter([a,b],c),midpoint([a,b])]))],'GD01').
def_inst(inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([a,c])])),['GD01']).
def_inst(inc(midpoint([a,c]),line([incenter([a,b],c),midpoint([a,c])])),['GD01']).
def(line([incenter([a,b],c),midpoint([a,c])]),[inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([a,c])])),inc(midpoint([a,c]),line([incenter([a,b],c),midpoint([a,c])]))],'GD01').
def_inst(inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([b,c])])),['GD01']).
def_inst(inc(midpoint([b,c]),line([incenter([a,b],c),midpoint([b,c])])),['GD01']).
def(line([incenter([a,b],c),midpoint([b,c])]),[inc(incenter([a,b],c),line([incenter([a,b],c),midpoint([b,c])])),inc(midpoint([b,c]),line([incenter([a,b],c),midpoint([b,c])]))],'GD01').
def_inst(inc(midpoint([a,b]),line([midpoint([a,b]),point_p(c,[a,b])])),['GD01']).
def_inst(inc(point_p(c,[a,b]),line([midpoint([a,b]),point_p(c,[a,b])])),['GD01']).
def(line([midpoint([a,b]),point_p(c,[a,b])]),[inc(midpoint([a,b]),line([midpoint([a,b]),point_p(c,[a,b])])),inc(point_p(c,[a,b]),line([midpoint([a,b]),point_p(c,[a,b])]))],'GD01').
def_inst(inc(midpoint([a,c]),line([midpoint([a,c]),point_p(b,[a,c])])),['GD01']).
def_inst(inc(point_p(b,[a,c]),line([midpoint([a,c]),point_p(b,[a,c])])),['GD01']).
def(line([midpoint([a,c]),point_p(b,[a,c])]),[inc(midpoint([a,c]),line([midpoint([a,c]),point_p(b,[a,c])])),inc(point_p(b,[a,c]),line([midpoint([a,c]),point_p(b,[a,c])]))],'GD01').
def_inst(inc(midpoint([b,c]),line([midpoint([b,c]),point_p(a,[b,c])])),['GD01']).
def_inst(inc(point_p(a,[b,c]),line([midpoint([b,c]),point_p(a,[b,c])])),['GD01']).
def(line([midpoint([b,c]),point_p(a,[b,c])]),[inc(midpoint([b,c]),line([midpoint([b,c]),point_p(a,[b,c])])),inc(point_p(a,[b,c]),line([midpoint([b,c]),point_p(a,[b,c])]))],'GD01').
def_inst(inc(c,line([c,foot(outcenter(c,[a,b]),[a,b])])),['GD01']).
def_inst(inc(foot(outcenter(c,[a,b]),[a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])])),['GD01']).
def(line([c,foot(outcenter(c,[a,b]),[a,b])]),[inc(c,line([c,foot(outcenter(c,[a,b]),[a,b])])),inc(foot(outcenter(c,[a,b]),[a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]))],'GD01').
def_inst(inc(b,line([b,foot(outcenter(b,[a,c]),[a,c])])),['GD01']).
def_inst(inc(foot(outcenter(b,[a,c]),[a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])])),['GD01']).
def(line([b,foot(outcenter(b,[a,c]),[a,c])]),[inc(b,line([b,foot(outcenter(b,[a,c]),[a,c])])),inc(foot(outcenter(b,[a,c]),[a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]))],'GD01').
def_inst(inc(a,line([a,foot(outcenter(a,[b,c]),[b,c])])),['GD01']).
def_inst(inc(foot(outcenter(a,[b,c]),[b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])])),['GD01']).
def(line([a,foot(outcenter(a,[b,c]),[b,c])]),[inc(a,line([a,foot(outcenter(a,[b,c]),[b,c])])),inc(foot(outcenter(a,[b,c]),[b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]))],'GD01').
def_inst(inc(a,line([a,c])),['GD01']).
def_inst(inc(c,line([a,c])),['GD01']).
def(line([a,c]),[inc(a,line([a,c])),inc(c,line([a,c]))],'GD01').
def_inst(inc(b,line([b,c])),['GD01']).
def_inst(inc(c,line([b,c])),['GD01']).
def(line([b,c]),[inc(b,line([b,c])),inc(c,line([b,c]))],'GD01').
def_inst(inc(a,line([a,b])),['GD01']).
def_inst(inc(b,line([a,b])),['GD01']).
def(line([a,b]),[inc(a,line([a,b])),inc(b,line([a,b]))],'GD01').
def_inst(inc_k(c,circle_center_through(euler(c,[a,b]),c)),['GD02']).
def_inst(center(euler(c,[a,b]),circle_center_through(euler(c,[a,b]),c)),['GD02']).
def(circle_center_through(euler(c,[a,b]),c),[inc_k(c,circle_center_through(euler(c,[a,b]),c)),center(euler(c,[a,b]),circle_center_through(euler(c,[a,b]),c))],'GD02').
def_inst(inc_k(b,circle_center_through(euler(b,[a,c]),b)),['GD02']).
def_inst(center(euler(b,[a,c]),circle_center_through(euler(b,[a,c]),b)),['GD02']).
def(circle_center_through(euler(b,[a,c]),b),[inc_k(b,circle_center_through(euler(b,[a,c]),b)),center(euler(b,[a,c]),circle_center_through(euler(b,[a,c]),b))],'GD02').
def_inst(inc_k(a,circle_center_through(euler(a,[b,c]),a)),['GD02']).
def_inst(center(euler(a,[b,c]),circle_center_through(euler(a,[b,c]),a)),['GD02']).
def(circle_center_through(euler(a,[b,c]),a),[inc_k(a,circle_center_through(euler(a,[b,c]),a)),center(euler(a,[b,c]),circle_center_through(euler(a,[b,c]),a))],'GD02').
def_inst(inc_k(c,circle_center_through(midpoint([a,c]),c)),['GD02']).
def_inst(center(midpoint([a,c]),circle_center_through(midpoint([a,c]),c)),['GD02']).
def(circle_center_through(midpoint([a,c]),c),[inc_k(c,circle_center_through(midpoint([a,c]),c)),center(midpoint([a,c]),circle_center_through(midpoint([a,c]),c))],'GD02').
def_inst(inc_k(a,circle_center_through(midpoint([a,b]),a)),['GD02']).
def_inst(center(midpoint([a,b]),circle_center_through(midpoint([a,b]),a)),['GD02']).
def(circle_center_through(midpoint([a,b]),a),[inc_k(a,circle_center_through(midpoint([a,b]),a)),center(midpoint([a,b]),circle_center_through(midpoint([a,b]),a))],'GD02').
def_inst(inc_k(b,circle_center_through(midpoint([b,c]),b)),['GD02']).
def_inst(center(midpoint([b,c]),circle_center_through(midpoint([b,c]),b)),['GD02']).
def(circle_center_through(midpoint([b,c]),b),[inc_k(b,circle_center_through(midpoint([b,c]),b)),center(midpoint([b,c]),circle_center_through(midpoint([b,c]),b))],'GD02').
def_inst(inc_k(b,circle_center_through(point_n(c,[a,b]),b)),['GD02']).
def_inst(center(point_n(c,[a,b]),circle_center_through(point_n(c,[a,b]),b)),['GD02']).
def(circle_center_through(point_n(c,[a,b]),b),[inc_k(b,circle_center_through(point_n(c,[a,b]),b)),center(point_n(c,[a,b]),circle_center_through(point_n(c,[a,b]),b))],'GD02').
def_inst(inc_k(a,circle_center_through(point_n(b,[a,c]),a)),['GD02']).
def_inst(center(point_n(b,[a,c]),circle_center_through(point_n(b,[a,c]),a)),['GD02']).
def(circle_center_through(point_n(b,[a,c]),a),[inc_k(a,circle_center_through(point_n(b,[a,c]),a)),center(point_n(b,[a,c]),circle_center_through(point_n(b,[a,c]),a))],'GD02').
def_inst(inc_k(c,circle_center_through(point_n(a,[b,c]),c)),['GD02']).
def_inst(center(point_n(a,[b,c]),circle_center_through(point_n(a,[b,c]),c)),['GD02']).
def(circle_center_through(point_n(a,[b,c]),c),[inc_k(c,circle_center_through(point_n(a,[b,c]),c)),center(point_n(a,[b,c]),circle_center_through(point_n(a,[b,c]),c))],'GD02').
def_inst(inc_k(foot(angle_bis_foot(c,[a,b]),line([a,c])),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['GD02']).
def_inst(center(angle_bis_foot(c,[a,b]),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['GD02']).
def(circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c]))),[inc_k(foot(angle_bis_foot(c,[a,b]),line([a,c])),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),center(angle_bis_foot(c,[a,b]),circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c]))))],'GD02').
def_inst(inc_k(foot(angle_bis_foot(b,[a,c]),line([a,b])),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['GD02']).
def_inst(center(angle_bis_foot(b,[a,c]),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['GD02']).
def(circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b]))),[inc_k(foot(angle_bis_foot(b,[a,c]),line([a,b])),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),center(angle_bis_foot(b,[a,c]),circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b]))))],'GD02').
def_inst(inc_k(foot(angle_bis_foot(a,[b,c]),line([a,b])),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['GD02']).
def_inst(center(angle_bis_foot(a,[b,c]),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['GD02']).
def(circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b]))),[inc_k(foot(angle_bis_foot(a,[b,c]),line([a,b])),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),center(angle_bis_foot(a,[b,c]),circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b]))))],'GD02').
def_inst(inc(circumcenter([a,b],c),side_bis([b,c])),['D1']).
def_inst(inc(circumcenter([a,b],c),side_bis([a,c])),['D1']).
def(circumcenter([a,b],c),[inc(circumcenter([a,b],c),side_bis([b,c])),inc(circumcenter([a,b],c),side_bis([a,c]))],'D1').
def_inst(inc(incenter([a,b],c),angle_bis(a,[b,c])),['D2']).
def_inst(inc(incenter([a,b],c),angle_bis(b,[a,c])),['D2']).
def(incenter([a,b],c),[inc(incenter([a,b],c),angle_bis(a,[b,c])),inc(incenter([a,b],c),angle_bis(b,[a,c]))],'D2').
def_inst(inc(orthocenter([a,b],c),altitude(a,[b,c])),['D3']).
def_inst(inc(orthocenter([a,b],c),altitude(b,[a,c])),['D3']).
def(orthocenter([a,b],c),[inc(orthocenter([a,b],c),altitude(a,[b,c])),inc(orthocenter([a,b],c),altitude(b,[a,c]))],'D3').
def_inst(inc(centroid([a,b],c),median(a,[b,c])),['D4']).
def_inst(inc(centroid([a,b],c),median(b,[a,c])),['D4']).
def(centroid([a,b],c),[inc(centroid([a,b],c),median(a,[b,c])),inc(centroid([a,b],c),median(b,[a,c]))],'D4').
def_inst(inc(foot(a,[b,c]),line([b,c])),['D5']).
def_inst(inc(foot(a,[b,c]),altitude(a,[b,c])),['D5']).
def(foot(a,[b,c]),[inc(foot(a,[b,c]),line([b,c])),inc(foot(a,[b,c]),altitude(a,[b,c]))],'D5').
def_inst(inc(foot(b,[a,c]),line([a,c])),['D6']).
def_inst(inc(foot(b,[a,c]),altitude(b,[a,c])),['D6']).
def(foot(b,[a,c]),[inc(foot(b,[a,c]),line([a,c])),inc(foot(b,[a,c]),altitude(b,[a,c]))],'D6').
def_inst(inc(foot(c,[a,b]),line([a,b])),['D7']).
def_inst(inc(foot(c,[a,b]),altitude(c,[a,b])),['D7']).
def(foot(c,[a,b]),[inc(foot(c,[a,b]),line([a,b])),inc(foot(c,[a,b]),altitude(c,[a,b]))],'D7').
def_inst(perp(altitude(a,[b,c]),line([b,c])),['D8']).
def_inst(inc(a,altitude(a,[b,c])),['D8']).
def(altitude(a,[b,c]),[perp(altitude(a,[b,c]),line([b,c])),inc(a,altitude(a,[b,c]))],'D8').
def_inst(perp(altitude(b,[a,c]),line([a,c])),['D9']).
def_inst(inc(b,altitude(b,[a,c])),['D9']).
def(altitude(b,[a,c]),[perp(altitude(b,[a,c]),line([a,c])),inc(b,altitude(b,[a,c]))],'D9').
def_inst(perp(altitude(c,[a,b]),line([a,b])),['D10']).
def_inst(inc(c,altitude(c,[a,b])),['D10']).
def(altitude(c,[a,b]),[perp(altitude(c,[a,b]),line([a,b])),inc(c,altitude(c,[a,b]))],'D10').
def_inst(perp(side_bis([b,c]),line([b,c])),['D11']).
def_inst(inc(midpoint([b,c]),side_bis([b,c])),['D11']).
def(side_bis([b,c]),[perp(side_bis([b,c]),line([b,c])),inc(midpoint([b,c]),side_bis([b,c]))],'D11').
def_inst(perp(side_bis([a,c]),line([a,c])),['D12']).
def_inst(inc(midpoint([a,c]),side_bis([a,c])),['D12']).
def(side_bis([a,c]),[perp(side_bis([a,c]),line([a,c])),inc(midpoint([a,c]),side_bis([a,c]))],'D12').
def_inst(perp(side_bis([a,b]),line([a,b])),['D13']).
def_inst(inc(midpoint([a,b]),side_bis([a,b])),['D13']).
def(side_bis([a,b]),[perp(side_bis([a,b]),line([a,b])),inc(midpoint([a,b]),side_bis([a,b]))],'D13').
def_inst(eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,0,0,0),['D14']).
def(angle_bis(a,[b,c]),[eq_angle_compound(angle(line([a,b]),angle_bis(a,[b,c])),angle(angle_bis(a,[b,c]),line([a,c])),1,0,0,0)],'D14').
def_inst(eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,0,0,0),['D15']).
def(angle_bis(b,[a,c]),[eq_angle_compound(angle(line([b,c]),angle_bis(b,[a,c])),angle(angle_bis(b,[a,c]),line([a,b])),1,0,0,0)],'D15').
def_inst(eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(angle_bis(c,[a,b]),line([b,c])),1,0,0,0),['D16']).
def(angle_bis(c,[a,b]),[eq_angle_compound(angle(line([a,c]),angle_bis(c,[a,b])),angle(angle_bis(c,[a,b]),line([b,c])),1,0,0,0)],'D16').
def_inst(inc(a,median(a,[b,c])),['D17']).
def_inst(inc(midpoint([b,c]),median(a,[b,c])),['D17']).
def(median(a,[b,c]),[inc(a,median(a,[b,c])),inc(midpoint([b,c]),median(a,[b,c]))],'D17').
def_inst(inc(b,median(b,[a,c])),['D18']).
def_inst(inc(midpoint([a,c]),median(b,[a,c])),['D18']).
def(median(b,[a,c]),[inc(b,median(b,[a,c])),inc(midpoint([a,c]),median(b,[a,c]))],'D18').
def_inst(inc(c,median(c,[a,b])),['D19']).
def_inst(inc(midpoint([a,b]),median(c,[a,b])),['D19']).
def(median(c,[a,b]),[inc(c,median(c,[a,b])),inc(midpoint([a,b]),median(c,[a,b]))],'D19').
def_inst(sratio(a,midpoint([a,b]),a,b,1,2),['D20']).
def(midpoint([a,b]),[sratio(a,midpoint([a,b]),a,b,1,2)],'D20').
def_inst(sratio(b,midpoint([b,c]),b,c,1,2),['D21']).
def(midpoint([b,c]),[sratio(b,midpoint([b,c]),b,c,1,2)],'D21').
def_inst(sratio(c,midpoint([a,c]),c,a,1,2),['D22']).
def(midpoint([a,c]),[sratio(c,midpoint([a,c]),c,a,1,2)],'D22').
def_inst(inc(angle_bis_foot(a,[b,c]),angle_bis(a,[b,c])),['D23']).
def_inst(inc(angle_bis_foot(a,[b,c]),line([b,c])),['D23']).
def(angle_bis_foot(a,[b,c]),[inc(angle_bis_foot(a,[b,c]),angle_bis(a,[b,c])),inc(angle_bis_foot(a,[b,c]),line([b,c]))],'D23').
def_inst(inc(angle_bis_foot(b,[a,c]),angle_bis(b,[a,c])),['D24']).
def_inst(inc(angle_bis_foot(b,[a,c]),line([a,c])),['D24']).
def(angle_bis_foot(b,[a,c]),[inc(angle_bis_foot(b,[a,c]),angle_bis(b,[a,c])),inc(angle_bis_foot(b,[a,c]),line([a,c]))],'D24').
def_inst(inc(angle_bis_foot(c,[a,b]),angle_bis(c,[a,b])),['D25']).
def_inst(inc(angle_bis_foot(c,[a,b]),line([a,b])),['D25']).
def(angle_bis_foot(c,[a,b]),[inc(angle_bis_foot(c,[a,b]),angle_bis(c,[a,b])),inc(angle_bis_foot(c,[a,b]),line([a,b]))],'D25').
def_inst(center(circumcenter([a,b],c),circumcircle([a,b],c)),['D26']).
def_inst(inc_k(c,circumcircle([a,b],c)),['D26']).
def(circumcircle([a,b],c),[center(circumcenter([a,b],c),circumcircle([a,b],c)),inc_k(c,circumcircle([a,b],c))],'D26').
def_inst(center(incenter([a,b],c),incircle([a,b],c)),['D27']).
def_inst(inc_k(foot(incenter([a,b],c),[b,c]),incircle([a,b],c)),['D27']).
def(incircle([a,b],c),[center(incenter([a,b],c),incircle([a,b],c)),inc_k(foot(incenter([a,b],c),[b,c]),incircle([a,b],c))],'D27').
def_inst(sratio(a,euler(a,[b,c]),a,orthocenter([a,b],c),1,2),['D28']).
def(euler(a,[b,c]),[sratio(a,euler(a,[b,c]),a,orthocenter([a,b],c),1,2)],'D28').
def_inst(sratio(b,euler(b,[a,c]),b,orthocenter([a,b],c),1,2),['D29']).
def(euler(b,[a,c]),[sratio(b,euler(b,[a,c]),b,orthocenter([a,b],c),1,2)],'D29').
def_inst(sratio(c,euler(c,[a,b]),c,orthocenter([a,b],c),1,2),['D30']).
def(euler(c,[a,b]),[sratio(c,euler(c,[a,b]),c,orthocenter([a,b],c),1,2)],'D30').
def_inst(sratio(orthocenter([a,b],c),npcenter([a,b],c),orthocenter([a,b],c),circumcenter([a,b],c),1,2),['D31']).
def(npcenter([a,b],c),[sratio(orthocenter([a,b],c),npcenter([a,b],c),orthocenter([a,b],c),circumcenter([a,b],c),1,2)],'D31').
def_inst(center(npcenter([a,b],c),npcircle([a,b],c)),['D32']).
def_inst(inc_k(midpoint([b,c]),npcircle([a,b],c)),['D32']).
def(npcircle([a,b],c),[center(npcenter([a,b],c),npcircle([a,b],c)),inc_k(midpoint([b,c]),npcircle([a,b],c))],'D32').
def_inst(inc(angle_bis_foot(a,[b,c]),line_a1),['D32']).
def_inst(perp_line_to_circ(line_a1,circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['D32']).
def(line_a1,[inc(angle_bis_foot(a,[b,c]),line_a1),perp_line_to_circ(line_a1,circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b]))))],'D32').
def_inst(inc(angle_bis_foot(a,[b,c]),line_a2),['D33']).
def_inst(perp_line_to_circ(line_a2,circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['D33']).
def(line_a2,[inc(angle_bis_foot(a,[b,c]),line_a2),perp_line_to_circ(line_a2,circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c]))))],'D33').
def_inst(inc(angle_bis_foot(b,[a,c]),line_b1),['D34']).
def_inst(perp_line_to_circ(line_b1,circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['D34']).
def(line_b1,[inc(angle_bis_foot(b,[a,c]),line_b1),perp_line_to_circ(line_b1,circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b]))))],'D34').
def_inst(inc(angle_bis_foot(b,[a,c]),line_b2),['D35']).
def_inst(perp_line_to_circ(line_b2,circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c])))),['D35']).
def(line_b2,[inc(angle_bis_foot(b,[a,c]),line_b2),perp_line_to_circ(line_b2,circle_center_through(angle_bis_foot(c,[a,b]),foot(angle_bis_foot(c,[a,b]),line([a,c]))))],'D35').
def_inst(inc(angle_bis_foot(c,[a,b]),line_c1),['D36']).
def_inst(perp_line_to_circ(line_c1,circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b])))),['D36']).
def(line_c1,[inc(angle_bis_foot(c,[a,b]),line_c1),perp_line_to_circ(line_c1,circle_center_through(angle_bis_foot(a,[b,c]),foot(angle_bis_foot(a,[b,c]),line([a,b]))))],'D36').
def_inst(inc(angle_bis_foot(c,[a,b]),line_c2),['D37']).
def_inst(perp_line_to_circ(line_c2,circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b])))),['D37']).
def(line_c2,[inc(angle_bis_foot(c,[a,b]),line_c2),perp_line_to_circ(line_c2,circle_center_through(angle_bis_foot(b,[a,c]),foot(angle_bis_foot(b,[a,c]),line([a,b]))))],'D37').
def_inst(inc_k(a_k,circumcircle([a,b],c)),['D38']).
def_inst(inc(a_k,altitude(a,[b,c])),['D38']).
def(a_k,[inc_k(a_k,circumcircle([a,b],c)),inc(a_k,altitude(a,[b,c]))],'D38').
def_inst(inc_k(b_k,circumcircle([a,b],c)),['D39']).
def_inst(inc(b_k,altitude(b,[a,c])),['D39']).
def(b_k,[inc_k(b_k,circumcircle([a,b],c)),inc(b_k,altitude(b,[a,c]))],'D39').
def_inst(inc_k(c_k,circumcircle([a,b],c)),['D40']).
def_inst(inc(c_k,altitude(c,[a,b])),['D40']).
def(c_k,[inc_k(c_k,circumcircle([a,b],c)),inc(c_k,altitude(c,[a,b]))],'D40').
def_inst(inc_k(chord_alt1(a),over_chord([angle_bis_foot(a,[b,c]),foot(b,[a,c])],angle(angle_bis(a,[b,c]),line([a,c])))),['D41']).
def_inst(inc(chord_alt1(a),altitude(a,[b,c])),['D41']).
def(chord_alt1(a),[inc_k(chord_alt1(a),over_chord([angle_bis_foot(a,[b,c]),foot(b,[a,c])],angle(angle_bis(a,[b,c]),line([a,c])))),inc(chord_alt1(a),altitude(a,[b,c]))],'D41').
def_inst(inc_k(chord_alt2(a),over_chord([angle_bis_foot(a,[b,c]),foot(c,[a,b])],angle(line([a,b]),angle_bis(a,[b,c])))),['D42']).
def_inst(inc(chord_alt2(a),altitude(a,[b,c])),['D42']).
def(chord_alt2(a),[inc_k(chord_alt2(a),over_chord([angle_bis_foot(a,[b,c]),foot(c,[a,b])],angle(line([a,b]),angle_bis(a,[b,c])))),inc(chord_alt2(a),altitude(a,[b,c]))],'D42').
def_inst(inc_k(chord_alt1(b),over_chord([angle_bis_foot(b,[a,c]),foot(c,[a,b])],angle(angle_bis(b,[a,c]),line([a,b])))),['D43']).
def_inst(inc(chord_alt1(b),altitude(b,[a,c])),['D43']).
def(chord_alt1(b),[inc_k(chord_alt1(b),over_chord([angle_bis_foot(b,[a,c]),foot(c,[a,b])],angle(angle_bis(b,[a,c]),line([a,b])))),inc(chord_alt1(b),altitude(b,[a,c]))],'D43').
def_inst(inc_k(chord_alt2(b),over_chord([angle_bis_foot(b,[a,c]),foot(a,[b,c])],angle(line([b,c]),angle_bis(b,[a,c])))),['D44']).
def_inst(inc(chord_alt2(b),altitude(b,[a,c])),['D44']).
def(chord_alt2(b),[inc_k(chord_alt2(b),over_chord([angle_bis_foot(b,[a,c]),foot(a,[b,c])],angle(line([b,c]),angle_bis(b,[a,c])))),inc(chord_alt2(b),altitude(b,[a,c]))],'D44').
def_inst(inc_k(chord_alt1(c),over_chord([angle_bis_foot(c,[a,b]),foot(a,[b,c])],angle(angle_bis(c,[a,b]),line([b,c])))),['D45']).
def_inst(inc(chord_alt1(c),altitude(c,[a,b])),['D45']).
def(chord_alt1(c),[inc_k(chord_alt1(c),over_chord([angle_bis_foot(c,[a,b]),foot(a,[b,c])],angle(angle_bis(c,[a,b]),line([b,c])))),inc(chord_alt1(c),altitude(c,[a,b]))],'D45').
def_inst(inc_k(chord_alt2(c),over_chord([angle_bis_foot(c,[a,b]),foot(b,[a,c])],angle(line([a,c]),angle_bis(c,[a,b])))),['D46']).
def_inst(inc(chord_alt2(c),altitude(c,[a,b])),['D46']).
def(chord_alt2(c),[inc_k(chord_alt2(c),over_chord([angle_bis_foot(c,[a,b]),foot(b,[a,c])],angle(line([a,c]),angle_bis(c,[a,b])))),inc(chord_alt2(c),altitude(c,[a,b]))],'D46').
def_inst(inc_k(point_n(a,[b,c]),circumcircle([a,b],c)),['D47']).
def_inst(inc(point_n(a,[b,c]),angle_bis(a,[b,c])),['D47']).
def(point_n(a,[b,c]),[inc_k(point_n(a,[b,c]),circumcircle([a,b],c)),inc(point_n(a,[b,c]),angle_bis(a,[b,c]))],'D47').
def_inst(inc_k(point_n(b,[a,c]),circumcircle([a,b],c)),['D48']).
def_inst(inc(point_n(b,[a,c]),angle_bis(b,[a,c])),['D48']).
def(point_n(b,[a,c]),[inc_k(point_n(b,[a,c]),circumcircle([a,b],c)),inc(point_n(b,[a,c]),angle_bis(b,[a,c]))],'D48').
def_inst(inc_k(point_n(c,[a,b]),circumcircle([a,b],c)),['D49']).
def_inst(inc(point_n(c,[a,b]),angle_bis(c,[a,b])),['D49']).
def(point_n(c,[a,b]),[inc_k(point_n(c,[a,b]),circumcircle([a,b],c)),inc(point_n(c,[a,b]),angle_bis(c,[a,b]))],'D49').
def_inst(inc_k(point_n_k(a,[b,c]),circumcircle([a,b],c)),['D50']).
def_inst(inc(point_n_k(a,[b,c]),side_bis([b,c])),['D50']).
def(point_n_k(a,[b,c]),[inc_k(point_n_k(a,[b,c]),circumcircle([a,b],c)),inc(point_n_k(a,[b,c]),side_bis([b,c]))],'D50').
def_inst(inc_k(point_n_k(b,[a,c]),circumcircle([a,b],c)),['D51']).
def_inst(inc(point_n_k(b,[a,c]),side_bis([a,c])),['D51']).
def(point_n_k(b,[a,c]),[inc_k(point_n_k(b,[a,c]),circumcircle([a,b],c)),inc(point_n_k(b,[a,c]),side_bis([a,c]))],'D51').
def_inst(inc_k(point_n_k(c,[a,b]),circumcircle([a,b],c)),['D52']).
def_inst(inc(point_n_k(c,[a,b]),side_bis([a,b])),['D52']).
def(point_n_k(c,[a,b]),[inc_k(point_n_k(c,[a,b]),circumcircle([a,b],c)),inc(point_n_k(c,[a,b]),side_bis([a,b]))],'D52').
def_inst(inc_k(a_w(b),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c]))),['D53']).
def_inst(inc(a_w(b),line([a,b])),['D53']).
def(a_w(b),[inc_k(a_w(b),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c]))),inc(a_w(b),line([a,b]))],'D53').
def_inst(inc_k(a_w(c),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c]))),['D54']).
def_inst(inc(a_w(c),line([a,c])),['D54']).
def(a_w(c),[inc_k(a_w(c),diam(angle_bis_foot(a,[b,c]),angle_bis_out_foot(a,[b,c]))),inc(a_w(c),line([a,c]))],'D54').
def_inst(inc_k(b_w(a),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c]))),['D55']).
def_inst(inc(b_w(a),line([a,b])),['D55']).
def(b_w(a),[inc_k(b_w(a),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c]))),inc(b_w(a),line([a,b]))],'D55').
def_inst(inc_k(b_w(c),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c]))),['D56']).
def_inst(inc(b_w(c),line([b,c])),['D56']).
def(b_w(c),[inc_k(b_w(c),diam(angle_bis_foot(b,[a,c]),angle_bis_out_foot(b,[a,c]))),inc(b_w(c),line([b,c]))],'D56').
def_inst(inc_k(c_w(a),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b]))),['D57']).
def_inst(inc(c_w(a),line([a,c])),['D57']).
def(c_w(a),[inc_k(c_w(a),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b]))),inc(c_w(a),line([a,c]))],'D57').
def_inst(inc_k(c_w(b),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b]))),['D58']).
def_inst(inc(c_w(b),line([b,c])),['D58']).
def(c_w(b),[inc_k(c_w(b),diam(angle_bis_foot(c,[a,b]),angle_bis_out_foot(c,[a,b]))),inc(c_w(b),line([b,c]))],'D58').
def_inst(inc_k(foot_out(a),diam(incenter([a,b],c),midpoint([b,c]))),['D59']).
def_inst(inc(foot_out(a),homothety(midpoint([b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1)),['D59']).
def(foot_out(a),[inc_k(foot_out(a),diam(incenter([a,b],c),midpoint([b,c]))),inc(foot_out(a),homothety(midpoint([b,c]),line([a,foot(outcenter(a,[b,c]),[b,c])]),-1,1))],'D59').
def_inst(inc_k(foot_out(b),diam(incenter([a,b],c),midpoint([a,c]))),['D60']).
def_inst(inc(foot_out(b),homothety(midpoint([a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1)),['D60']).
def(foot_out(b),[inc_k(foot_out(b),diam(incenter([a,b],c),midpoint([a,c]))),inc(foot_out(b),homothety(midpoint([a,c]),line([b,foot(outcenter(b,[a,c]),[a,c])]),-1,1))],'D60').
def_inst(inc_k(foot_out(c),diam(incenter([a,b],c),midpoint([a,b]))),['D61']).
def_inst(inc(foot_out(c),homothety(midpoint([a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1)),['D61']).
def(foot_out(c),[inc_k(foot_out(c),diam(incenter([a,b],c),midpoint([a,b]))),inc(foot_out(c),homothety(midpoint([a,b]),line([c,foot(outcenter(c,[a,b]),[a,b])]),-1,1))],'D61').
def_inst(inc_k(second_ai(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])))),['D62']).
def_inst(inc(second_ai(a),angle_bis(a,[b,c])),['D62']).
def(second_ai(a),[inc_k(second_ai(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(b,[a,c]),angle_bis(c,[a,b])))),inc(second_ai(a),angle_bis(a,[b,c]))],'D62').
def_inst(inc_k(second_ai(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])))),['D63']).
def_inst(inc(second_ai(b),angle_bis(b,[a,c])),['D63']).
def(second_ai(b),[inc_k(second_ai(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(angle_bis(c,[a,b]),angle_bis(a,[b,c])))),inc(second_ai(b),angle_bis(b,[a,c]))],'D63').
def_inst(inc_k(second_ai(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])))),['D64']).
def_inst(inc(second_ai(c),angle_bis(c,[a,b])),['D64']).
def(second_ai(c),[inc_k(second_ai(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(a,[b,c]),angle_bis(b,[a,c])))),inc(second_ai(c),angle_bis(c,[a,b]))],'D64').
def_inst(inc_k(foot_ima(a),diam(incenter([a,b],c),midpoint([b,c]))),['D65']).
def_inst(inc_k(foot_ima(a),incircle([a,b],c)),['D65']).
def(foot_ima(a),[inc_k(foot_ima(a),diam(incenter([a,b],c),midpoint([b,c]))),inc_k(foot_ima(a),incircle([a,b],c))],'D65').
def_inst(inc_k(foot_ima(b),diam(incenter([a,b],c),midpoint([a,c]))),['D66']).
def_inst(inc_k(foot_ima(b),incircle([a,b],c)),['D66']).
def(foot_ima(b),[inc_k(foot_ima(b),diam(incenter([a,b],c),midpoint([a,c]))),inc_k(foot_ima(b),incircle([a,b],c))],'D66').
def_inst(inc_k(foot_ima(c),diam(incenter([a,b],c),midpoint([a,b]))),['D67']).
def_inst(inc_k(foot_ima(c),incircle([a,b],c)),['D67']).
def(foot_ima(c),[inc_k(foot_ima(c),diam(incenter([a,b],c),midpoint([a,b]))),inc_k(foot_ima(c),incircle([a,b],c))],'D67').
def_inst(inc_k(chord1(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(line([a,b]),line([a,c])))),['D68']).
def_inst(inc_k(chord1(a),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(a,[b,c])))),['D68']).
def(chord1(a),[inc_k(chord1(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(line([a,b]),line([a,c])))),inc_k(chord1(a),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(a,[b,c]))))],'D68').
def_inst(inc_k(chord2(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(line([a,b]),line([a,c])))),['D69']).
def_inst(inc_k(chord2(a),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(a,[b,c])))),['D69']).
def(chord2(a),[inc_k(chord2(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(line([a,b]),line([a,c])))),inc_k(chord2(a),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(a,[b,c]))))],'D69').
def_inst(inc_k(chord3(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(c,[a,b]),angle_bis(b,[a,c])))),['D70']).
def_inst(inc_k(chord3(a),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(a,[b,c])))),['D70']).
def(chord3(a),[inc_k(chord3(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(c,[a,b]),angle_bis(b,[a,c])))),inc_k(chord3(a),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(a,[b,c]))))],'D70').
def_inst(inc_k(chord4(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(c,[a,b]),angle_bis(b,[a,c])))),['D71']).
def_inst(inc_k(chord4(a),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(a,[b,c])))),['D71']).
def(chord4(a),[inc_k(chord4(a),over_chord([angle_bis_foot(b,[a,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(c,[a,b]),angle_bis(b,[a,c])))),inc_k(chord4(a),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(a,[b,c]))))],'D71').
def_inst(inc_k(chord1(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(line([a,c]),line([b,c])))),['D72']).
def_inst(inc_k(chord1(c),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(c,[a,b])))),['D72']).
def(chord1(c),[inc_k(chord1(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(line([a,c]),line([b,c])))),inc_k(chord1(c),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(c,[a,b]))))],'D72').
def_inst(inc_k(chord2(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(line([a,c]),line([b,c])))),['D72']).
def_inst(inc_k(chord2(c),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(c,[a,b])))),['D72']).
def(chord2(c),[inc_k(chord2(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(line([a,c]),line([b,c])))),inc_k(chord2(c),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(c,[a,b]))))],'D72').
def_inst(inc_k(chord3(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(b,[a,c]),angle_bis(a,[b,c])))),['D73']).
def_inst(inc_k(chord3(c),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(c,[a,b])))),['D73']).
def(chord3(c),[inc_k(chord3(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(b,[a,c]),angle_bis(a,[b,c])))),inc_k(chord3(c),over_chord([angle_bis_foot(b,[a,c]),incenter([a,b],c)],angle(line([a,c]),angle_bis(c,[a,b]))))],'D73').
def_inst(inc_k(chord4(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(b,[a,c]),angle_bis(a,[b,c])))),['D74']).
def_inst(inc_k(chord4(c),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(c,[a,b])))),['D74']).
def(chord4(c),[inc_k(chord4(c),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(b,[a,c])],angle(angle_bis(b,[a,c]),angle_bis(a,[b,c])))),inc_k(chord4(c),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(c,[a,b]))))],'D74').
def_inst(inc_k(chord1(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(line([b,c]),line([a,b])))),['D75']).
def_inst(inc_k(chord1(b),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(b,[a,c])))),['D75']).
def(chord1(b),[inc_k(chord1(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(line([b,c]),line([a,b])))),inc_k(chord1(b),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(b,[a,c]))))],'D75').
def_inst(inc_k(chord2(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(line([b,c]),line([a,b])))),['D76']).
def_inst(inc_k(chord2(b),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(b,[a,c])))),['D76']).
def(chord2(b),[inc_k(chord2(b),over_chord([angle_bis_foot(c,[a,b]),angle_bis_foot(a,[b,c])],angle(line([b,c]),line([a,b])))),inc_k(chord2(b),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(b,[a,c]))))],'D76').
def_inst(inc_k(chord3(b),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(a,[b,c]),angle_bis(c,[a,b])))),['D77']).
def_inst(inc_k(chord3(b),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(b,[a,c])))),['D77']).
def(chord3(b),[inc_k(chord3(b),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(a,[b,c]),angle_bis(c,[a,b])))),inc_k(chord3(b),over_chord([angle_bis_foot(a,[b,c]),incenter([a,b],c)],angle(line([b,c]),angle_bis(b,[a,c]))))],'D77').
def_inst(inc_k(chord4(b),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(a,[b,c]),angle_bis(c,[a,b])))),['D78']).
def_inst(inc_k(chord4(b),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(b,[a,c])))),['D78']).
def(chord4(b),[inc_k(chord4(b),over_chord([angle_bis_foot(a,[b,c]),angle_bis_foot(c,[a,b])],angle(angle_bis(a,[b,c]),angle_bis(c,[a,b])))),inc_k(chord4(b),over_chord([angle_bis_foot(c,[a,b]),incenter([a,b],c)],angle(line([a,b]),angle_bis(b,[a,c]))))],'D78').
def_inst(inc(point_p(a,[b,c]),altitude(a,[b,c])),['D79']).
def_inst(inc_k(point_p(a,[b,c]),circle_center_through(euler(a,[b,c]),midpoint([b,c]))),['D79']).
def(point_p(a,[b,c]),[inc(point_p(a,[b,c]),altitude(a,[b,c])),inc_k(point_p(a,[b,c]),circle_center_through(euler(a,[b,c]),midpoint([b,c])))],'D79').
def_inst(inc(point_p(b,[a,c]),altitude(b,[a,c])),['D80']).
def_inst(inc_k(point_p(b,[a,c]),circle_center_through(euler(b,[a,c]),midpoint([a,c]))),['D80']).
def(point_p(b,[a,c]),[inc(point_p(b,[a,c]),altitude(b,[a,c])),inc_k(point_p(b,[a,c]),circle_center_through(euler(b,[a,c]),midpoint([a,c])))],'D80').
def_inst(inc(point_p(c,[a,b]),altitude(c,[a,b])),['D81']).
def_inst(inc_k(point_p(c,[a,b]),circle_center_through(euler(c,[a,b]),midpoint([a,b]))),['D81']).
def(point_p(c,[a,b]),[inc(point_p(c,[a,b]),altitude(c,[a,b])),inc_k(point_p(c,[a,b]),circle_center_through(euler(c,[a,b]),midpoint([a,b])))],'D81').
def_inst(inc(point_p1(a,[b,c]),altitude(a,[b,c])),['D82']).
def_inst(inc_k(point_p1(a,[b,c]),circle_center_through(euler(a,[b,c]),midpoint([b,c]))),['D82']).
def(point_p1(a,[b,c]),[inc(point_p1(a,[b,c]),altitude(a,[b,c])),inc_k(point_p1(a,[b,c]),circle_center_through(euler(a,[b,c]),midpoint([b,c])))],'D82').
def_inst(inc(point_p1(b,[a,c]),altitude(b,[a,c])),['D83']).
def_inst(inc_k(point_p1(b,[a,c]),circle_center_through(euler(b,[a,c]),midpoint([a,c]))),['D83']).
def(point_p1(b,[a,c]),[inc(point_p1(b,[a,c]),altitude(b,[a,c])),inc_k(point_p1(b,[a,c]),circle_center_through(euler(b,[a,c]),midpoint([a,c])))],'D83').
def_inst(inc(point_p1(c,[a,b]),altitude(c,[a,b])),['D84']).
def_inst(inc_k(point_p1(c,[a,b]),circle_center_through(euler(c,[a,b]),midpoint([a,b]))),['D84']).
def(point_p1(c,[a,b]),[inc(point_p1(c,[a,b]),altitude(c,[a,b])),inc_k(point_p1(c,[a,b]),circle_center_through(euler(c,[a,b]),midpoint([a,b])))],'D84').
def_inst(inc(midpoint([b,c]),line_x1),['D85']).
def_inst(perp_line_to_circ(line_x1,incircle([a,b],c)),['D85']).
def(line_x1,[inc(midpoint([b,c]),line_x1),perp_line_to_circ(line_x1,incircle([a,b],c))],'D85').
def_inst(inc(midpoint([a,c]),line_x2),['D86']).
def_inst(perp_line_to_circ(line_x2,incircle([a,b],c)),['D86']).
def(line_x2,[inc(midpoint([a,c]),line_x2),perp_line_to_circ(line_x2,incircle([a,b],c))],'D86').
def_inst(inc(midpoint([a,b]),line_x3),['D87']).
def_inst(perp_line_to_circ(line_x3,incircle([a,b],c)),['D87']).
def(line_x3,[inc(midpoint([a,b]),line_x3),perp_line_to_circ(line_x3,incircle([a,b],c))],'D87').
def_inst(inc(foot(a,[b,c]),line_y1),['D88']).
def_inst(perp_line_to_circ(line_y1,incircle([a,b],c)),['D88']).
def(line_y1,[inc(foot(a,[b,c]),line_y1),perp_line_to_circ(line_y1,incircle([a,b],c))],'D88').
def_inst(inc(foot(b,[a,c]),line_y2),['D89']).
def_inst(perp_line_to_circ(line_y2,incircle([a,b],c)),['D89']).
def(line_y2,[inc(foot(b,[a,c]),line_y2),perp_line_to_circ(line_y2,incircle([a,b],c))],'D89').
def_inst(inc(foot(c,[a,b]),line_y3),['D90']).
def_inst(perp_line_to_circ(line_y3,incircle([a,b],c)),['D90']).
def(line_y3,[inc(foot(c,[a,b]),line_y3),perp_line_to_circ(line_y3,incircle([a,b],c))],'D90').
