Construction in GCLC language

dim 120 120

point H_{a} 80 40
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10


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

color 200 200 200
drawline a
color 0 0 0




% Constructing a point B such that H_{a}B/H_{a}T_{a}=0.0560637570073179
towards B H_{a} T_{a} 0.0560637570073179 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H_{a} T_{a} 
color 0 0 0



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

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




% Constructing a point P_{\_G19668} with coordinates (10,30)
point P_{\_G19668} 10 30 
cmark_r P_{\_G19668}

% Constructing a line L_{\_G19671} which passes through point B and point H_{a}
line L_{\_G19671} B H_{a} 

color 200 200 200
drawline L_{\_G19671}
color 0 0 0


% Constructing a line L_{\_G19674} which is perpendicular to line L_{\_G19671} and which passes through point H_{a}
perp L_{\_G19674} H_{a} L_{\_G19671} 

color 200 200 200
drawline L_{\_G19674}
color 0 0 0


% Constructing a line L_{\_G19677} which passes through point B and point P_{\_G19668}
line L_{\_G19677} B P_{\_G19668} 

color 200 200 200
drawline L_{\_G19677}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G19677} and line L_{\_G19674}
intersec A L_{\_G19677} L_{\_G19674} 
cmark_t A


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point T_{a} is not incident to the line c
% Constructing a point P_{\_G20050} which is a foot of the point T_{a} on the line c
foot P_{\_G20050} T_{a} c 
cmark_r P_{\_G20050}
color 200 200 200
drawline T_{a} P_{\_G20050} 
color 0 0 0

% Constructing a circle k(T_{a},foot[T_{a},c]) whose center is at point T_{a} and which passes through point P_{\_G20050}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G20050} 

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



% NDG:  point A is outside the circle k(T_{a},foot[T_{a},c])
% Constructing a point P_{\_G20441} which is a foot of the point T_{a} on the line c
foot P_{\_G20441} T_{a} c 
cmark_r P_{\_G20441}
color 200 200 200
drawline T_{a} P_{\_G20441} 
color 0 0 0

% Constructing a line L_{\_G20444} which passes through point T_{a} and point A
line L_{\_G20444} T_{a} A 

color 200 200 200
drawline L_{\_G20444}
color 0 0 0


% Constructing a point P_{\_G20447} which is an image of the point P_{\_G20441} in the symmetry to point/line L_{\_G20444}
sim P_{\_G20447} L_{\_G20444} P_{\_G20441} 
cmark_r P_{\_G20447}

% Constructing a line b which passes through point A and point P_{\_G20447}
line b A P_{\_G20447} 

color 200 200 200
drawline b
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; point A is outside the circle k(T_{a},foot[T_{a},c]); point T_{a} is not incident to the line c
% Determination conditions:  lines b and a are not the same; points A and B are not the same; points H_{a} and T_{a} are not the same