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 O is given by the problem setting, but it has to belong to the line m_{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 m_{c} which is perpendicular to line c and which passes through point M_{c}
perp m_{c} M_{c} c 

color 200 200 200
drawline m_{c}
color 0 0 0




% Constructing a point P_{\_G35779} with coordinates (10,30)
point P_{\_G35779} 10 30 
cmark_r P_{\_G35779}

% Constructing a line L_{\_G35782} which passes through point H_{c} and point M_{c}
line L_{\_G35782} H_{c} M_{c} 

color 200 200 200
drawline L_{\_G35782}
color 0 0 0


% Constructing a line L_{\_G35785} which is perpendicular to line L_{\_G35782} and which passes through point M_{c}
perp L_{\_G35785} M_{c} L_{\_G35782} 

color 200 200 200
drawline L_{\_G35785}
color 0 0 0


% Constructing a line L_{\_G35788} which passes through point H_{c} and point P_{\_G35779}
line L_{\_G35788} H_{c} P_{\_G35779} 

color 200 200 200
drawline L_{\_G35788}
color 0 0 0


% Constructing a point O which belongs to line L_{\_G35788} and line L_{\_G35785}
intersec O L_{\_G35788} L_{\_G35785} 
color 220 0 0
fontsize 11
cmark_t O
color 0 0 0
fontsize 10




% 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 A such that M_{c}A/M_{c}H_{c}=0.07024359863822825
towards A M_{c} H_{c} 0.07024359863822825 
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


% NDG:  points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line h_{c} and circle k(O,C) intersect
% Constructing points C and C_{k} which are in intersection of k(O,C) and h_{c}
intersec2 C C_{k} k(O,C) h_{c} 
cmark_b C
cmark_r C_{k}



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line h_{c} and circle k(O,C) intersect; points A and O are not the same
% Determination conditions:  points M_{c} and H_{c} are not the same