Construction in GCLC language

dim 120 120

point C 110 40
point M_{b} 95 67.5
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

cmark_b C
cmark_rt M_{b}
cmark_lt T_{c}
color 0 0 0
fontsize 10


% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C A 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



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

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_{\_G62487} which is a foot of the point T_{c} on the line b
foot P_{\_G62487} T_{c} b 
cmark_r P_{\_G62487}
color 200 200 200
drawline T_{c} P_{\_G62487} 
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_{\_G62487}
circle k(T_{c},foot[T_{c},b]) T_{c} P_{\_G62487} 

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_{\_G62878} which is a foot of the point T_{c} on the line b
foot P_{\_G62878} T_{c} b 
cmark_r P_{\_G62878}
color 200 200 200
drawline T_{c} P_{\_G62878} 
color 0 0 0

% Constructing a line L_{\_G62881} which passes through point T_{c} and point C
line L_{\_G62881} T_{c} C 

color 200 200 200
drawline L_{\_G62881}
color 0 0 0


% Constructing a point P_{\_G62884} which is an image of the point P_{\_G62878} in the symmetry to point/line L_{\_G62881}
sim P_{\_G62884} L_{\_G62881} P_{\_G62878} 
cmark_r P_{\_G62884}

% Constructing a line a which passes through point C and point P_{\_G62884}
line a C P_{\_G62884} 

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