Construction in GCLC language

dim 120 120

point A 80 95
point M_{b} 95 67.5
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

cmark_t A
cmark_rt M_{b}
cmark_lt T_{c}
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 A and T_{c} are not the same
% Constructing a line c which passes through point A and point T_{c}
line c A T_{c} 

color 200 200 200
drawline c
color 0 0 0



% NDG:  point T_{c} is not incident to the line b
% Constructing a point P_{\_G13971} which is a foot of the point T_{c} on the line b
foot P_{\_G13971} T_{c} b 
cmark_r P_{\_G13971}
color 200 200 200
drawline T_{c} P_{\_G13971} 
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_{\_G13971}
circle k(T_{c},foot[T_{c},b]) T_{c} P_{\_G13971} 

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_{\_G14362} which is a foot of the point T_{c} on the line b
foot P_{\_G14362} T_{c} b 
cmark_r P_{\_G14362}
color 200 200 200
drawline T_{c} P_{\_G14362} 
color 0 0 0

% Constructing a line L_{\_G14365} which passes through point T_{c} and point C
line L_{\_G14365} T_{c} C 

color 200 200 200
drawline L_{\_G14365}
color 0 0 0


% Constructing a point P_{\_G14368} which is an image of the point P_{\_G14362} in the symmetry to point/line L_{\_G14365}
sim P_{\_G14368} L_{\_G14365} P_{\_G14362} 
cmark_r P_{\_G14368}

% Constructing a line a which passes through point C and point P_{\_G14368}
line a C P_{\_G14368} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a 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 b
% Determination conditions:  lines a and c are not the same; points A and T_{c} are not the same; points A and M_{b} are not the same