Construction in GCLC language

dim 120 120

point M_{a} 65 40
point H_{c} 68.91 84.83
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_lt H_{c}
cmark_lt T_{c}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0



% NDG:  line c and circle k(M_{a},B) intersect% DET:  points H_{c} and B must be different
% Constructing a point P_{\_G54423} which is a foot of the point M_{a} on the line c
foot P_{\_G54423} M_{a} c 
cmark_r P_{\_G54423}
color 200 200 200
drawline M_{a} P_{\_G54423} 
color 0 0 0

% Constructing a point B which is an image of the point H_{c} in the symmetry to point/line P_{\_G54423}
sim B P_{\_G54423} H_{c} 
cmark_b B



% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point T_{c} is not incident to the line a
% Constructing a point P_{\_G54707} which is a foot of the point T_{c} on the line a
foot P_{\_G54707} T_{c} a 
cmark_r P_{\_G54707}
color 200 200 200
drawline T_{c} P_{\_G54707} 
color 0 0 0

% Constructing a circle k(T_{c},foot[T_{c},b]) whose center is at point T_{c} and which passes through point P_{\_G54707}
circle k(T_{c},foot[T_{c},b]) T_{c} P_{\_G54707} 

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



% NDG:  point C is outside the circle k(T_{c},foot[T_{c},b])
% Constructing a point P_{\_G55098} which is a foot of the point T_{c} on the line a
foot P_{\_G55098} T_{c} a 
cmark_r P_{\_G55098}
color 200 200 200
drawline T_{c} P_{\_G55098} 
color 0 0 0

% Constructing a line L_{\_G55101} which passes through point T_{c} and point C
line L_{\_G55101} T_{c} C 

color 200 200 200
drawline L_{\_G55101}
color 0 0 0


% Constructing a point P_{\_G55104} which is an image of the point P_{\_G55098} in the symmetry to point/line L_{\_G55101}
sim P_{\_G55104} L_{\_G55101} P_{\_G55098} 
cmark_r P_{\_G55104}

% Constructing a line b which passes through point C and point P_{\_G55104}
line b C P_{\_G55104} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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