Construction in GCLC language

dim 120 120

point C 110 40
point M_{b} 95 67.5
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_b C
cmark_rt M_{b}
cmark_b T_{a}
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 C and T_{a} are not the same
% Constructing a line a which passes through point C and point T_{a}
line a C T_{a} 

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_{\_G54997} which is a foot of the point T_{a} on the line b
foot P_{\_G54997} T_{a} b 
cmark_r P_{\_G54997}
color 200 200 200
drawline T_{a} P_{\_G54997} 
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_{\_G54997}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G54997} 

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_{\_G55388} which is a foot of the point T_{a} on the line b
foot P_{\_G55388} T_{a} b 
cmark_r P_{\_G55388}
color 200 200 200
drawline T_{a} P_{\_G55388} 
color 0 0 0

% Constructing a line L_{\_G55391} which passes through point T_{a} and point A
line L_{\_G55391} T_{a} A 

color 200 200 200
drawline L_{\_G55391}
color 0 0 0


% Constructing a point P_{\_G55394} which is an image of the point P_{\_G55388} in the symmetry to point/line L_{\_G55391}
sim P_{\_G55394} L_{\_G55391} P_{\_G55388} 
cmark_r P_{\_G55394}

% Constructing a line c which passes through point A and point P_{\_G55394}
line c A P_{\_G55394} 

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