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 C 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 C such that H_{a}C/H_{a}T_{a}=0.8554931445385381
towards C H_{a} T_{a} 0.8554931445385381 
color 220 0 0
fontsize 11
cmark_b C
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_{\_G63130} with coordinates (10,30)
point P_{\_G63130} 10 30 
cmark_r P_{\_G63130}

% Constructing a line L_{\_G63133} which passes through point C and point H_{a}
line L_{\_G63133} C H_{a} 

color 200 200 200
drawline L_{\_G63133}
color 0 0 0


% Constructing a line L_{\_G63136} which is perpendicular to line L_{\_G63133} and which passes through point H_{a}
perp L_{\_G63136} H_{a} L_{\_G63133} 

color 200 200 200
drawline L_{\_G63136}
color 0 0 0


% Constructing a line L_{\_G63139} which passes through point C and point P_{\_G63130}
line L_{\_G63139} C P_{\_G63130} 

color 200 200 200
drawline L_{\_G63139}
color 0 0 0


% Constructing a point A which belongs to line L_{\_G63139} and line L_{\_G63136}
intersec A L_{\_G63139} L_{\_G63136} 
cmark_t A


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point T_{a} is not incident to the line b
% Constructing a point P_{\_G63512} which is a foot of the point T_{a} on the line b
foot P_{\_G63512} T_{a} b 
cmark_r P_{\_G63512}
color 200 200 200
drawline T_{a} P_{\_G63512} 
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_{\_G63512}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G63512} 

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_{\_G63903} which is a foot of the point T_{a} on the line b
foot P_{\_G63903} T_{a} b 
cmark_r P_{\_G63903}
color 200 200 200
drawline T_{a} P_{\_G63903} 
color 0 0 0

% Constructing a line L_{\_G63906} which passes through point T_{a} and point A
line L_{\_G63906} T_{a} A 

color 200 200 200
drawline L_{\_G63906}
color 0 0 0


% Constructing a point P_{\_G63909} which is an image of the point P_{\_G63903} in the symmetry to point/line L_{\_G63906}
sim P_{\_G63909} L_{\_G63906} P_{\_G63903} 
cmark_r P_{\_G63909}

% Constructing a line c which passes through point A and point P_{\_G63909}
line c A P_{\_G63909} 

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