Construction in GCLC language

dim 120 120

point B 20 40
point M_{c} 50 67.5
point T_{a} 70.86 40

color 220 0 0
fontsize 11

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


% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point T_{a} is not incident to the line c
% Constructing a point P_{\_G30102} which is a foot of the point T_{a} on the line c
foot P_{\_G30102} T_{a} c 
cmark_r P_{\_G30102}
color 200 200 200
drawline T_{a} P_{\_G30102} 
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_{\_G30102}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G30102} 

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_{\_G30493} which is a foot of the point T_{a} on the line c
foot P_{\_G30493} T_{a} c 
cmark_r P_{\_G30493}
color 200 200 200
drawline T_{a} P_{\_G30493} 
color 0 0 0

% Constructing a line L_{\_G30496} which passes through point T_{a} and point A
line L_{\_G30496} T_{a} A 

color 200 200 200
drawline L_{\_G30496}
color 0 0 0


% Constructing a point P_{\_G30499} which is an image of the point P_{\_G30493} in the symmetry to point/line L_{\_G30496}
sim P_{\_G30499} L_{\_G30496} P_{\_G30493} 
cmark_r P_{\_G30499}

% Constructing a line b which passes through point A and point P_{\_G30499}
line b A P_{\_G30499} 

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 B and T_{a} are not the same; points B and M_{c} are not the same