Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_lt H_{c}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline h_{c}
color 0 0 0




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

color 200 200 200
drawline c
color 0 0 0




% Constructing a point P_{\_G16597} with coordinates (10,30)
point P_{\_G16597} 10 30 
cmark_r P_{\_G16597}

% Constructing a line L_{\_G16600} which passes through point E_{c} and point H_{c}
line L_{\_G16600} E_{c} H_{c} 

color 200 200 200
drawline L_{\_G16600}
color 0 0 0


% Constructing a line L_{\_G16603} which is perpendicular to line L_{\_G16600} and which passes through point H_{c}
perp L_{\_G16603} H_{c} L_{\_G16600} 

color 200 200 200
drawline L_{\_G16603}
color 0 0 0


% Constructing a line L_{\_G16606} which passes through point E_{c} and point P_{\_G16597}
line L_{\_G16606} E_{c} P_{\_G16597} 

color 200 200 200
drawline L_{\_G16606}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G16606} and line L_{\_G16603}
intersec B L_{\_G16606} L_{\_G16603} 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10



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

color 200 200 200
drawline m(BH_{c})
color 0 0 0

color 200 200 200
drawsegment B H_{c} 
color 0 0 0


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

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

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



% Constructing a point A such that BA/BH_{c}=0.30455204580233136
towards A B H_{c} 0.30455204580233136 
cmark_t A
color 200 200 200
drawsegment B H_{c} 
color 0 0 0



% Constructing a point M_{c} such that AM_{c}/AB=0.5
towards M_{c} A B 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment A B 
color 0 0 0


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

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



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


% NDG:  points E_{c} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{c}
circle k(N,M_{a}) N E_{c} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line m(BH_{c}) and circle k(N,M_{a}) intersect
% Constructing points M_{a} and E_{b} which are in intersection of k(N,M_{a}) and m(BH_{c})
intersec2 M_{a} E_{b} k(N,M_{a}) m(BH_{c}) 
cmark_b M_{a}
cmark_r E_{b}



% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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