Construction in GCLC language

dim 120 120

point A 80 95
point M_{b} 95 67.5
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_t A
cmark_rt M_{b}
cmark_b T_{a}
color 0 0 0
fontsize 10


% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point T_{a} is not incident to the line b
% Constructing a point P_{\_G10426} which is a foot of the point T_{a} on the line b
foot P_{\_G10426} T_{a} b 
cmark_r P_{\_G10426}
color 200 200 200
drawline T_{a} P_{\_G10426} 
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_{\_G10426}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G10426} 

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_{\_G10817} which is a foot of the point T_{a} on the line b
foot P_{\_G10817} T_{a} b 
cmark_r P_{\_G10817}
color 200 200 200
drawline T_{a} P_{\_G10817} 
color 0 0 0

% Constructing a line L_{\_G10820} which passes through point T_{a} and point A
line L_{\_G10820} T_{a} A 

color 200 200 200
drawline L_{\_G10820}
color 0 0 0


% Constructing a point P_{\_G10823} which is an image of the point P_{\_G10817} in the symmetry to point/line L_{\_G10820}
sim P_{\_G10823} L_{\_G10820} P_{\_G10817} 
cmark_r P_{\_G10823}

% Constructing a line c which passes through point A and point P_{\_G10823}
line c A P_{\_G10823} 

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 T_{a} and C are not the same; points A and M_{b} are not the same