Construction in GCLC language

dim 120 120

point C 110 40
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_b 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_{C,2/3}(c) which is constructible from the others objects given 
% DET:  points C and H_{c} are not the same
% Constructing a line h_{c} which passes through point C and point H_{c}
line h_{c} C H_{c} 

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




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

color 200 200 200
drawline c
color 0 0 0




% Constructing a point P_{\_G41998} such that CP_{\_G41998}/CH_{c}=0.6666666666666666
towards P_{\_G41998} C H_{c} 0.6666666666666666 
cmark_r P_{\_G41998}
color 200 200 200
drawsegment C H_{c} 
color 0 0 0

% Constructing a line h_{C,2/3}(c) which contains the point P_{\_G41998} and is parallel to the line c
parallel h_{C,2/3}(c) P_{\_G41998} c 

color 200 200 200
drawline h_{C,2/3}(c)
color 0 0 0




% Constructing a point P_{\_G42356} such that CP_{\_G42356}/CH_{c}=0.6666666666666666
towards P_{\_G42356} C H_{c} 0.6666666666666666 
cmark_r P_{\_G42356}
color 200 200 200
drawsegment C H_{c} 
color 0 0 0

% Constructing a point P_{\_G42359} with coordinates (10,30)
point P_{\_G42359} 10 30 
cmark_r P_{\_G42359}

% Constructing a line L_{\_G42362} which passes through point C and point P_{\_G42356}
line L_{\_G42362} C P_{\_G42356} 

color 200 200 200
drawline L_{\_G42362}
color 0 0 0


% Constructing a line L_{\_G42365} which is perpendicular to line L_{\_G42362} and which passes through point P_{\_G42356}
perp L_{\_G42365} P_{\_G42356} L_{\_G42362} 

color 200 200 200
drawline L_{\_G42365}
color 0 0 0


% Constructing a line L_{\_G42368} which passes through point C and point P_{\_G42359}
line L_{\_G42368} C P_{\_G42359} 

color 200 200 200
drawline L_{\_G42368}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G42368} and line L_{\_G42365}
intersec G L_{\_G42368} L_{\_G42365} 
color 220 0 0
fontsize 11
cmark_t G
color 0 0 0
fontsize 10




% Constructing a point M_{c} such that GM_{c}/GC=-0.5
towards M_{c} G C -0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c} 
color 0 0 0



% Constructing a point A such that H_{c}A/H_{c}M_{c}=0.22479628249960223
towards A H_{c} M_{c} 0.22479628249960223 
cmark_t A
color 200 200 200
drawsegment H_{c} M_{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 C and H_{c} are not the same