Construction in GCLC language

dim 120 120

point M_{a} 65 40
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_b M_{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_{M_{a},1/3}(h_{a}) which is constructible from the others objects given 
% DET:  points M_{a} and H_{a} are not the same
% Constructing a line a which passes through point M_{a} and point H_{a}
line a M_{a} 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_{\_G38501} such that M_{a}P_{\_G38501}/M_{a}H_{a}=0.3333333333333333
towards P_{\_G38501} M_{a} H_{a} 0.3333333333333333 
cmark_r P_{\_G38501}
color 200 200 200
drawsegment M_{a} H_{a} 
color 0 0 0

% Constructing a line h_{M_{a},1/3}(h_{a}) which contains the point P_{\_G38501} and is parallel to the line h_{a}
parallel h_{M_{a},1/3}(h_{a}) P_{\_G38501} h_{a} 

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




% Constructing a point P_{\_G38874} such that M_{a}P_{\_G38874}/M_{a}H_{a}=0.3333333333333333
towards P_{\_G38874} M_{a} H_{a} 0.3333333333333333 
cmark_r P_{\_G38874}
color 200 200 200
drawsegment M_{a} H_{a} 
color 0 0 0

% Constructing a point P_{\_G38877} with coordinates (10,30)
point P_{\_G38877} 10 30 
cmark_r P_{\_G38877}

% Constructing a line L_{\_G38880} which passes through point M_{a} and point P_{\_G38874}
line L_{\_G38880} M_{a} P_{\_G38874} 

color 200 200 200
drawline L_{\_G38880}
color 0 0 0


% Constructing a line L_{\_G38883} which is perpendicular to line L_{\_G38880} and which passes through point P_{\_G38874}
perp L_{\_G38883} P_{\_G38874} L_{\_G38880} 

color 200 200 200
drawline L_{\_G38883}
color 0 0 0


% Constructing a line L_{\_G38886} which passes through point M_{a} and point P_{\_G38877}
line L_{\_G38886} M_{a} P_{\_G38877} 

color 200 200 200
drawline L_{\_G38886}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G38886} and line L_{\_G38883}
intersec G L_{\_G38886} L_{\_G38883} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point A such that GA/GM_{a}=-2
towards A G M_{a} -2 
cmark_t A
color 200 200 200
drawsegment M_{a} A 
color 0 0 0



% Constructing a point B such that M_{a}B/M_{a}H_{a}=0.8058305105119898
towards B M_{a} H_{a} 0.8058305105119898 
cmark_b B
color 200 200 200
drawsegment M_{a} H_{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 M_{a} and H_{a} are not the same