Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_lt H_{c}
color 0 0 0
fontsize 10


% point G is given by the problem setting, but it has to belong to the line h_{M_{c},1/3}(h_{c}) which is constructible from the others objects given 
% DET:  points M_{c} and H_{c} are not the same
% Constructing a line c which passes through point M_{c} and point H_{c}
line c M_{c} H_{c} 

color 200 200 200
drawline c
color 0 0 0




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

color 200 200 200
drawline h_{c}
color 0 0 0




% Constructing a point P_{\_G55118} such that M_{c}P_{\_G55118}/M_{c}H_{c}=0.3333333333333333
towards P_{\_G55118} M_{c} H_{c} 0.3333333333333333 
cmark_r P_{\_G55118}
color 200 200 200
drawsegment M_{c} H_{c} 
color 0 0 0

% Constructing a line h_{M_{c},1/3}(h_{c}) which contains the point P_{\_G55118} and is parallel to the line h_{c}
parallel h_{M_{c},1/3}(h_{c}) P_{\_G55118} h_{c} 

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




% Constructing a point P_{\_G55491} such that M_{c}P_{\_G55491}/M_{c}H_{c}=0.3333333333333333
towards P_{\_G55491} M_{c} H_{c} 0.3333333333333333 
cmark_r P_{\_G55491}
color 200 200 200
drawsegment M_{c} H_{c} 
color 0 0 0

% Constructing a point P_{\_G55494} with coordinates (10,30)
point P_{\_G55494} 10 30 
cmark_r P_{\_G55494}

% Constructing a line L_{\_G55497} which passes through point M_{c} and point P_{\_G55491}
line L_{\_G55497} M_{c} P_{\_G55491} 

color 200 200 200
drawline L_{\_G55497}
color 0 0 0


% Constructing a line L_{\_G55500} which is perpendicular to line L_{\_G55497} and which passes through point P_{\_G55491}
perp L_{\_G55500} P_{\_G55491} L_{\_G55497} 

color 200 200 200
drawline L_{\_G55500}
color 0 0 0


% Constructing a line L_{\_G55503} which passes through point M_{c} and point P_{\_G55494}
line L_{\_G55503} M_{c} P_{\_G55494} 

color 200 200 200
drawline L_{\_G55503}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G55503} and line L_{\_G55500}
intersec G L_{\_G55503} L_{\_G55500} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point C such that GC/GM_{c}=-2
towards C G M_{c} -2 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



% Constructing a point A such that M_{c}A/M_{c}H_{c}=0.7138703597808984
towards A M_{c} H_{c} 0.7138703597808984 
cmark_t A
color 200 200 200
drawsegment M_{c} H_{c} 
color 0 0 0



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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