Construction in GCLC language

dim 120 120

point B 20 40
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_b 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_{B,2/3}(b) which is constructible from the others objects given 
% DET:  points B and H_{b} are not the same
% Constructing a line h_{b} which passes through point B and point H_{b}
line h_{b} 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_{\_G29682} such that BP_{\_G29682}/BH_{b}=0.6666666666666666
towards P_{\_G29682} B H_{b} 0.6666666666666666 
cmark_r P_{\_G29682}
color 200 200 200
drawsegment B H_{b} 
color 0 0 0

% Constructing a line h_{B,2/3}(b) which contains the point P_{\_G29682} and is parallel to the line b
parallel h_{B,2/3}(b) P_{\_G29682} b 

color 200 200 200
drawline h_{B,2/3}(b)
color 0 0 0




% Constructing a point P_{\_G30040} such that BP_{\_G30040}/BH_{b}=0.6666666666666666
towards P_{\_G30040} B H_{b} 0.6666666666666666 
cmark_r P_{\_G30040}
color 200 200 200
drawsegment B H_{b} 
color 0 0 0

% Constructing a point P_{\_G30043} with coordinates (10,30)
point P_{\_G30043} 10 30 
cmark_r P_{\_G30043}

% Constructing a line L_{\_G30046} which passes through point B and point P_{\_G30040}
line L_{\_G30046} B P_{\_G30040} 

color 200 200 200
drawline L_{\_G30046}
color 0 0 0


% Constructing a line L_{\_G30049} which is perpendicular to line L_{\_G30046} and which passes through point P_{\_G30040}
perp L_{\_G30049} P_{\_G30040} L_{\_G30046} 

color 200 200 200
drawline L_{\_G30049}
color 0 0 0


% Constructing a line L_{\_G30052} which passes through point B and point P_{\_G30043}
line L_{\_G30052} B P_{\_G30043} 

color 200 200 200
drawline L_{\_G30052}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G30052} and line L_{\_G30049}
intersec G L_{\_G30052} L_{\_G30049} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point M_{b} such that GM_{b}/GB=-0.5
towards M_{b} G B -0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0



% Constructing a point A such that H_{b}A/H_{b}M_{b}=0.10254536217125466
towards A H_{b} M_{b} 0.10254536217125466 
cmark_t A
color 200 200 200
drawsegment H_{b} M_{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 B and H_{b} are not the same