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 A is given by the problem setting, but it has to belong to the line 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 point A such that H_{b}A/H_{b}T_{b}=0.2756056975379441
towards A H_{b} T_{b} 0.2756056975379441 
color 220 0 0
fontsize 11
cmark_t A
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H_{b} T_{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_{\_G27690} with coordinates (10,30)
point P_{\_G27690} 10 30 
cmark_r P_{\_G27690}

% Constructing a line L_{\_G27693} which passes through point A and point H_{b}
line L_{\_G27693} A H_{b} 

color 200 200 200
drawline L_{\_G27693}
color 0 0 0


% Constructing a line L_{\_G27696} which is perpendicular to line L_{\_G27693} and which passes through point H_{b}
perp L_{\_G27696} H_{b} L_{\_G27693} 

color 200 200 200
drawline L_{\_G27696}
color 0 0 0


% Constructing a line L_{\_G27699} which passes through point A and point P_{\_G27690}
line L_{\_G27699} A P_{\_G27690} 

color 200 200 200
drawline L_{\_G27699}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G27699} and line L_{\_G27696}
intersec B L_{\_G27699} L_{\_G27696} 
cmark_b B


% DET:  points B and A are not the same
% Constructing a line c which passes through point B and point A
line c B A 

color 200 200 200
drawline c
color 0 0 0



% NDG:  point T_{b} is not incident to the line c
% Constructing a point P_{\_G28072} which is a foot of the point T_{b} on the line c
foot P_{\_G28072} T_{b} c 
cmark_r P_{\_G28072}
color 200 200 200
drawline T_{b} P_{\_G28072} 
color 0 0 0

% Constructing a circle k(T_{b},foot[T_{b},c]) whose center is at point T_{b} and which passes through point P_{\_G28072}
circle k(T_{b},foot[T_{b},c]) T_{b} P_{\_G28072} 

color 200 200 200
drawcircle k(T_{b},foot[T_{b},c])
color 0 0 0



% NDG:  point B is outside the circle k(T_{b},foot[T_{b},c])
% Constructing a point P_{\_G28463} which is a foot of the point T_{b} on the line c
foot P_{\_G28463} T_{b} c 
cmark_r P_{\_G28463}
color 200 200 200
drawline T_{b} P_{\_G28463} 
color 0 0 0

% Constructing a line L_{\_G28466} which passes through point T_{b} and point B
line L_{\_G28466} T_{b} B 

color 200 200 200
drawline L_{\_G28466}
color 0 0 0


% Constructing a point P_{\_G28469} which is an image of the point P_{\_G28463} in the symmetry to point/line L_{\_G28466}
sim P_{\_G28469} L_{\_G28466} P_{\_G28463} 
cmark_r P_{\_G28469}

% Constructing a line a which passes through point B and point P_{\_G28469}
line a B P_{\_G28469} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a and b are not parallel; point B is outside the circle k(T_{b},foot[T_{b},c]); point T_{b} is not incident to the line c
% Determination conditions:  lines a and b are not the same; points B and A are not the same; points H_{b} and T_{b} are not the same