Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_rt M_{b}
cmark_rt H_{b}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline b
color 0 0 0




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

color 200 200 200
drawline m_{b}
color 0 0 0




% Constructing a point P_{\_G60132} with coordinates (10,30)
point P_{\_G60132} 10 30 
cmark_r P_{\_G60132}

% Constructing a line L_{\_G60135} which passes through point H_{b} and point M_{b}
line L_{\_G60135} H_{b} M_{b} 

color 200 200 200
drawline L_{\_G60135}
color 0 0 0


% Constructing a line L_{\_G60138} which is perpendicular to line L_{\_G60135} and which passes through point M_{b}
perp L_{\_G60138} M_{b} L_{\_G60135} 

color 200 200 200
drawline L_{\_G60138}
color 0 0 0


% Constructing a line L_{\_G60141} which passes through point H_{b} and point P_{\_G60132}
line L_{\_G60141} H_{b} P_{\_G60132} 

color 200 200 200
drawline L_{\_G60141}
color 0 0 0


% Constructing a point O which belongs to line L_{\_G60141} and line L_{\_G60138}
intersec O L_{\_G60141} L_{\_G60138} 
color 220 0 0
fontsize 11
cmark_t O
color 0 0 0
fontsize 10




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

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




% Constructing a point A such that M_{b}A/M_{b}H_{b}=0.34350414555676084
towards A M_{b} H_{b} 0.34350414555676084 
cmark_t A
color 200 200 200
drawsegment M_{b} H_{b} 
color 0 0 0



% 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


% 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 h_{b} and circle k(O,C) intersect
% Constructing points B_{k} and B which are in intersection of k(O,C) and h_{b}
intersec2 B_{k} B k(O,C) h_{b} 
cmark_r B_{k}
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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