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 A 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_{\_G12009} with coordinates (10,30)
point P_{\_G12009} 10 30 
cmark_r P_{\_G12009}

% Constructing a line L_{\_G12012} which passes through point E_{c} and point H_{c}
line L_{\_G12012} E_{c} H_{c} 

color 200 200 200
drawline L_{\_G12012}
color 0 0 0


% Constructing a line L_{\_G12015} which is perpendicular to line L_{\_G12012} and which passes through point H_{c}
perp L_{\_G12015} H_{c} L_{\_G12012} 

color 200 200 200
drawline L_{\_G12015}
color 0 0 0


% Constructing a line L_{\_G12018} which passes through point E_{c} and point P_{\_G12009}
line L_{\_G12018} E_{c} P_{\_G12009} 

color 200 200 200
drawline L_{\_G12018}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G12018} and line L_{\_G12015}
intersec A L_{\_G12018} L_{\_G12015} 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10



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

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

color 200 200 200
drawsegment A 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 B such that AB/AH_{c}=0.5977027121627259
towards B A H_{c} 0.5977027121627259 
cmark_b B
color 200 200 200
drawsegment A H_{c} 
color 0 0 0



% Constructing a point M_{c} such that BM_{c}/BA=0.5
towards M_{c} B A 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment B A 
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(AH_{c}) and circle k(N,M_{a}) intersect
% Constructing points M_{b} and E_{a} which are in intersection of k(N,M_{a}) and m(AH_{c})
intersec2 M_{b} E_{a} k(N,M_{a}) m(AH_{c}) 
cmark_rt M_{b}
cmark_r E_{a}



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line m(AH_{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 A and H_{c} are not the same; points E_{c} and H_{c} are not the same