Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_rt T_{b}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline b
color 0 0 0




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

color 200 200 200
drawline h_{b}
color 0 0 0




% Constructing a point P_{\_G47517} with coordinates (10,30)
point P_{\_G47517} 10 30 
cmark_r P_{\_G47517}

% Constructing a line L_{\_G47520} which passes through point T_{b} and point H_{b}
line L_{\_G47520} T_{b} H_{b} 

color 200 200 200
drawline L_{\_G47520}
color 0 0 0


% Constructing a line L_{\_G47523} which is perpendicular to line L_{\_G47520} and which passes through point H_{b}
perp L_{\_G47523} H_{b} L_{\_G47520} 

color 200 200 200
drawline L_{\_G47523}
color 0 0 0


% Constructing a line L_{\_G47526} which passes through point T_{b} and point P_{\_G47517}
line L_{\_G47526} T_{b} P_{\_G47517} 

color 200 200 200
drawline L_{\_G47526}
color 0 0 0


% Constructing a point H which belongs to line L_{\_G47526} and line L_{\_G47523}
intersec H L_{\_G47526} L_{\_G47523} 
color 220 0 0
fontsize 11
cmark_rt H
color 0 0 0
fontsize 10




% Constructing a point A such that H_{b}A/H_{b}T_{b}=0.0704087450943216
towards A H_{b} T_{b} 0.0704087450943216 
cmark_t A
color 200 200 200
drawsegment H_{b} T_{b} 
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




% Constructing a point B such that HB/HH_{b}=0.0704087450943216
towards B H H_{b} 0.0704087450943216 
cmark_b B
color 200 200 200
drawsegment H H_{b} 
color 0 0 0



% Constructing a point M_{c} such that BM_{c}/BA=0.5
towards M_{c} B A 0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment B A 
color 0 0 0


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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line h_{a} and circle k(M_{c},A) intersect% DET:  points A and H_{a} must be different
% Constructing a point P_{\_G48291} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G48291} M_{c} h_{a} 
cmark_r P_{\_G48291}
color 200 200 200
drawline M_{c} P_{\_G48291} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G48291}
sim H_{a} P_{\_G48291} A 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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