Construction in GCLC language

dim 120 120

point B 20 40
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_b B
cmark_b H_{a}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline a
color 0 0 0




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

color 200 200 200
drawline h_{a}
color 0 0 0




% Constructing a point P_{\_G5745} with coordinates (10,30)
point P_{\_G5745} 10 30 
cmark_r P_{\_G5745}

% Constructing a line L_{\_G5748} which passes through point B and point H_{a}
line L_{\_G5748} B H_{a} 

color 200 200 200
drawline L_{\_G5748}
color 0 0 0


% Constructing a line L_{\_G5751} which is perpendicular to line L_{\_G5748} and which passes through point H_{a}
perp L_{\_G5751} H_{a} L_{\_G5748} 

color 200 200 200
drawline L_{\_G5751}
color 0 0 0


% Constructing a line L_{\_G5754} which passes through point B and point P_{\_G5745}
line L_{\_G5754} B P_{\_G5745} 

color 200 200 200
drawline L_{\_G5754}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G5754} and line L_{\_G5751}
intersec A L_{\_G5754} L_{\_G5751} 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10




% Constructing a point C such that BC/BH_{a}=0.5823970040618319
towards C B H_{a} 0.5823970040618319 
cmark_b C
color 200 200 200
drawsegment B H_{a} 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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