Construction in GCLC language

dim 120 120

point H_{a} 80 40
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_b M_{a}
color 0 0 0
fontsize 10


% point E_{a} is given by the problem setting, but it has to belong to the line h_{a} which is constructible from the others objects given 
% DET:  points H_{a} and M_{a} are not the same
% Constructing a line a which passes through point H_{a} and point M_{a}
line a H_{a} M_{a} 

color 200 200 200
drawline a
color 0 0 0




% Constructing a line h_{a} which is perpendicular to line a and which passes through point H_{a}
perp h_{a} H_{a} a 

color 200 200 200
drawline h_{a}
color 0 0 0




% Constructing a point P_{\_G61392} with coordinates (10,30)
point P_{\_G61392} 10 30 
cmark_r P_{\_G61392}

% Constructing a line L_{\_G61395} which passes through point M_{a} and point H_{a}
line L_{\_G61395} M_{a} H_{a} 

color 200 200 200
drawline L_{\_G61395}
color 0 0 0


% Constructing a line L_{\_G61398} which is perpendicular to line L_{\_G61395} and which passes through point H_{a}
perp L_{\_G61398} H_{a} L_{\_G61395} 

color 200 200 200
drawline L_{\_G61398}
color 0 0 0


% Constructing a line L_{\_G61401} which passes through point M_{a} and point P_{\_G61392}
line L_{\_G61401} M_{a} P_{\_G61392} 

color 200 200 200
drawline L_{\_G61401}
color 0 0 0


% Constructing a point E_{a} which belongs to line L_{\_G61401} and line L_{\_G61398}
intersec E_{a} L_{\_G61401} L_{\_G61398} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10



% DET:  points E_{a} and M_{a} are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point E_{a} and point M_{a}
line m(H_{b}H_{c}) E_{a} M_{a} 

color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0



% DET:  points E_{a} and H_{a} are not the same
% Constructing bisector m(E_{a}H_{a}) of the segment E_{a}H_{a}
med m(E_{a}H_{a}) E_{a} H_{a} 

color 200 200 200
drawline m(E_{a}H_{a})
color 0 0 0

color 200 200 200
drawsegment E_{a} H_{a} 
color 0 0 0


% NDG:  lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not parallel% DET:  lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{a}H_{a}) and line m(H_{b}H_{c})
intersec N m(E_{a}H_{a}) m(H_{b}H_{c}) 
cmark_r N



% Constructing a point A such that E_{a}A/E_{a}H_{a}=0.48869117352315006
towards A E_{a} H_{a} 0.48869117352315006 
cmark_t A
color 200 200 200
drawsegment E_{a} H_{a} 
color 0 0 0



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0



% Constructing a point O such that NO/NH=-1
towards O N H -1 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


% NDG:  points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line a and circle k(O,C) intersect; points A and O are not the same; lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not parallel
% Determination conditions:  lines m(E_{a}H_{a}) and m(H_{b}H_{c}) are not the same; points E_{a} and H_{a} are not the same; points E_{a} and M_{a} are not the same; points H_{a} and M_{a} are not the same