Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point H 80 72.73

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_rt H
color 0 0 0
fontsize 10


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

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




% Constructing a point C such that H_{c}C/H_{c}H=0.977273227745791
towards C H_{c} H 0.977273227745791 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H_{c} H 
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_{\_G44005} with coordinates (10,30)
point P_{\_G44005} 10 30 
cmark_r P_{\_G44005}

% Constructing a line L_{\_G44008} which passes through point C and point H_{c}
line L_{\_G44008} C H_{c} 

color 200 200 200
drawline L_{\_G44008}
color 0 0 0


% Constructing a line L_{\_G44011} which is perpendicular to line L_{\_G44008} and which passes through point H_{c}
perp L_{\_G44011} H_{c} L_{\_G44008} 

color 200 200 200
drawline L_{\_G44011}
color 0 0 0


% Constructing a line L_{\_G44014} which passes through point C and point P_{\_G44005}
line L_{\_G44014} C P_{\_G44005} 

color 200 200 200
drawline L_{\_G44014}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G44014} and line L_{\_G44011}
intersec A L_{\_G44014} L_{\_G44011} 
cmark_t A



% Constructing a point M_{b} such that AM_{b}/AC=0.5
towards M_{b} A C 0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment A C 
color 0 0 0


% DET:  points A and H are not the same
% Constructing a line h_{a} which passes through point A and point H
line h_{a} A H 

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



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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  line h_{a} and circle k(M_{b},C) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G44615} which is a foot of the point M_{b} on the line h_{a}
foot P_{\_G44615} M_{b} h_{a} 
cmark_r P_{\_G44615}
color 200 200 200
drawline M_{b} P_{\_G44615} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G44615}
sim H_{a} P_{\_G44615} A 
cmark_b H_{a}


% DET:  points H_{a} and C are not the same
% Constructing a line a which passes through point H_{a} and point C
line a H_{a} C 

color 200 200 200
drawline a
color 0 0 0



% NDG:  lines c and a are not parallel% DET:  lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines c and a are not parallel; line h_{a} and circle k(M_{b},C) intersect; points A and M_{b} are not the same
% Determination conditions:  lines c and a are not the same; points H_{a} and C are not the same; points A and H_{a} must be different; points A and H are not the same; points H_{c} and H are not the same