Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H_{b}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline h_{b}
color 0 0 0




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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point P_{\_G31368} with coordinates (10,30)
point P_{\_G31368} 10 30 
cmark_r P_{\_G31368}

% Constructing a line L_{\_G31371} which passes through point E_{b} and point H_{b}
line L_{\_G31371} E_{b} H_{b} 

color 200 200 200
drawline L_{\_G31371}
color 0 0 0


% Constructing a line L_{\_G31374} which is perpendicular to line L_{\_G31371} and which passes through point H_{b}
perp L_{\_G31374} H_{b} L_{\_G31371} 

color 200 200 200
drawline L_{\_G31374}
color 0 0 0


% Constructing a line L_{\_G31377} which passes through point E_{b} and point P_{\_G31368}
line L_{\_G31377} E_{b} P_{\_G31368} 

color 200 200 200
drawline L_{\_G31377}
color 0 0 0


% Constructing a point C which belongs to line L_{\_G31377} and line L_{\_G31374}
intersec C L_{\_G31377} L_{\_G31374} 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10



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

color 200 200 200
drawline m(CH_{b})
color 0 0 0

color 200 200 200
drawsegment C H_{b} 
color 0 0 0


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

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

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



% Constructing a point A such that CA/CH_{b}=0.3116337202237696
towards A C H_{b} 0.3116337202237696 
cmark_t A
color 200 200 200
drawsegment C H_{b} 
color 0 0 0



% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


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

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



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


% NDG:  points E_{b} 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_{b}
circle k(N,M_{a}) N E_{b} 

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



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



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



drawsegment A B
drawsegment A C
drawsegment B C

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