Construction in GCLC language

dim 120 120

point B 20 40
point M_{a} 65 40
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

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


% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point T_{b} is not incident to the line a
% Constructing a point P_{\_G26625} which is a foot of the point T_{b} on the line a
foot P_{\_G26625} T_{b} a 
cmark_r P_{\_G26625}
color 200 200 200
drawline T_{b} P_{\_G26625} 
color 0 0 0

% Constructing a circle k(T_{b},foot[T_{b},c]) whose center is at point T_{b} and which passes through point P_{\_G26625}
circle k(T_{b},foot[T_{b},c]) T_{b} P_{\_G26625} 

color 200 200 200
drawcircle k(T_{b},foot[T_{b},c])
color 0 0 0



% NDG:  point B is outside the circle k(T_{b},foot[T_{b},c])
% Constructing a point P_{\_G27016} which is a foot of the point T_{b} on the line a
foot P_{\_G27016} T_{b} a 
cmark_r P_{\_G27016}
color 200 200 200
drawline T_{b} P_{\_G27016} 
color 0 0 0

% Constructing a line L_{\_G27019} which passes through point T_{b} and point B
line L_{\_G27019} T_{b} B 

color 200 200 200
drawline L_{\_G27019}
color 0 0 0


% Constructing a point P_{\_G27022} which is an image of the point P_{\_G27016} in the symmetry to point/line L_{\_G27019}
sim P_{\_G27022} L_{\_G27019} P_{\_G27016} 
cmark_r P_{\_G27022}

% Constructing a line c which passes through point B and point P_{\_G27022}
line c B P_{\_G27022} 

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines c and b are not parallel; point B is outside the circle k(T_{b},foot[T_{b},c]); point T_{b} is not incident to the line a
% Determination conditions:  lines c and b are not the same; points T_{b} and C are not the same; points B and M_{a} are not the same