Construction in GCLC language

dim 120 120

point A 80 95
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_t A
cmark_b H_{a}
color 0 0 0
fontsize 10


% point G is given by the problem setting, but it has to belong to the line h_{A,2/3}(a) which is constructible from the others objects given 
% DET:  points A and H_{a} are not the same
% Constructing a line h_{a} which passes through point A and point H_{a}
line h_{a} A H_{a} 

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




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

color 200 200 200
drawline a
color 0 0 0




% Constructing a point P_{\_G13051} such that AP_{\_G13051}/AH_{a}=0.6666666666666666
towards P_{\_G13051} A H_{a} 0.6666666666666666 
cmark_r P_{\_G13051}
color 200 200 200
drawsegment A H_{a} 
color 0 0 0

% Constructing a line h_{A,2/3}(a) which contains the point P_{\_G13051} and is parallel to the line a
parallel h_{A,2/3}(a) P_{\_G13051} a 

color 200 200 200
drawline h_{A,2/3}(a)
color 0 0 0




% Constructing a point P_{\_G13409} such that AP_{\_G13409}/AH_{a}=0.6666666666666666
towards P_{\_G13409} A H_{a} 0.6666666666666666 
cmark_r P_{\_G13409}
color 200 200 200
drawsegment A H_{a} 
color 0 0 0

% Constructing a point P_{\_G13412} with coordinates (10,30)
point P_{\_G13412} 10 30 
cmark_r P_{\_G13412}

% Constructing a line L_{\_G13415} which passes through point A and point P_{\_G13409}
line L_{\_G13415} A P_{\_G13409} 

color 200 200 200
drawline L_{\_G13415}
color 0 0 0


% Constructing a line L_{\_G13418} which is perpendicular to line L_{\_G13415} and which passes through point P_{\_G13409}
perp L_{\_G13418} P_{\_G13409} L_{\_G13415} 

color 200 200 200
drawline L_{\_G13418}
color 0 0 0


% Constructing a line L_{\_G13421} which passes through point A and point P_{\_G13412}
line L_{\_G13421} A P_{\_G13412} 

color 200 200 200
drawline L_{\_G13421}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G13421} and line L_{\_G13418}
intersec G L_{\_G13421} L_{\_G13418} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point M_{a} such that GM_{a}/GA=-0.5
towards M_{a} G A -0.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0



% Constructing a point B such that H_{a}B/H_{a}M_{a}=0.4313565660722055
towards B H_{a} M_{a} 0.4313565660722055 
cmark_b B
color 200 200 200
drawsegment H_{a} M_{a} 
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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