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 G is given by the problem setting, but it has to belong to the line h_{M_{b},1/3}(h_{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 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 P_{\_G48715} such that M_{b}P_{\_G48715}/M_{b}H_{b}=0.3333333333333333
towards P_{\_G48715} M_{b} H_{b} 0.3333333333333333 
cmark_r P_{\_G48715}
color 200 200 200
drawsegment M_{b} H_{b} 
color 0 0 0

% Constructing a line h_{M_{b},1/3}(h_{b}) which contains the point P_{\_G48715} and is parallel to the line h_{b}
parallel h_{M_{b},1/3}(h_{b}) P_{\_G48715} h_{b} 

color 200 200 200
drawline h_{M_{b},1/3}(h_{b})
color 0 0 0




% Constructing a point P_{\_G49088} such that M_{b}P_{\_G49088}/M_{b}H_{b}=0.3333333333333333
towards P_{\_G49088} M_{b} H_{b} 0.3333333333333333 
cmark_r P_{\_G49088}
color 200 200 200
drawsegment M_{b} H_{b} 
color 0 0 0

% Constructing a point P_{\_G49091} with coordinates (10,30)
point P_{\_G49091} 10 30 
cmark_r P_{\_G49091}

% Constructing a line L_{\_G49094} which passes through point M_{b} and point P_{\_G49088}
line L_{\_G49094} M_{b} P_{\_G49088} 

color 200 200 200
drawline L_{\_G49094}
color 0 0 0


% Constructing a line L_{\_G49097} which is perpendicular to line L_{\_G49094} and which passes through point P_{\_G49088}
perp L_{\_G49097} P_{\_G49088} L_{\_G49094} 

color 200 200 200
drawline L_{\_G49097}
color 0 0 0


% Constructing a line L_{\_G49100} which passes through point M_{b} and point P_{\_G49091}
line L_{\_G49100} M_{b} P_{\_G49091} 

color 200 200 200
drawline L_{\_G49100}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G49100} and line L_{\_G49097}
intersec G L_{\_G49100} L_{\_G49097} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point B such that GB/GM_{b}=-2
towards B G M_{b} -2 
cmark_b B
color 200 200 200
drawsegment M_{b} B 
color 0 0 0



% Constructing a point A such that M_{b}A/M_{b}H_{b}=0.8123107802342717
towards A M_{b} H_{b} 0.8123107802342717 
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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions: 
% Determination conditions:  points M_{b} and H_{b} are not the same