Construction in GCLC language

dim 120 120

point M_{a} 65 40
point H_{b} 89.36 77.83
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline b
color 0 0 0



% NDG:  points H_{b} and M_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point H_{b}
circle k(M_{a},B) M_{a} H_{b} 

color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0



% NDG:  line b and circle k(M_{a},B) intersect% DET:  points H_{b} and C must be different
% Constructing a point P_{\_G44072} which is a foot of the point M_{a} on the line b
foot P_{\_G44072} M_{a} b 
cmark_r P_{\_G44072}
color 200 200 200
drawline M_{a} P_{\_G44072} 
color 0 0 0

% Constructing a point C which is an image of the point H_{b} in the symmetry to point/line P_{\_G44072}
sim C P_{\_G44072} H_{b} 
cmark_b C



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


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point T_{b} is not incident to the line a
% Constructing a point P_{\_G44356} which is a foot of the point T_{b} on the line a
foot P_{\_G44356} T_{b} a 
cmark_r P_{\_G44356}
color 200 200 200
drawline T_{b} P_{\_G44356} 
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_{\_G44356}
circle k(T_{b},foot[T_{b},c]) T_{b} P_{\_G44356} 

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_{\_G44747} which is a foot of the point T_{b} on the line a
foot P_{\_G44747} T_{b} a 
cmark_r P_{\_G44747}
color 200 200 200
drawline T_{b} P_{\_G44747} 
color 0 0 0

% Constructing a line L_{\_G44750} which passes through point T_{b} and point B
line L_{\_G44750} T_{b} B 

color 200 200 200
drawline L_{\_G44750}
color 0 0 0


% Constructing a point P_{\_G44753} which is an image of the point P_{\_G44747} in the symmetry to point/line L_{\_G44750}
sim P_{\_G44753} L_{\_G44750} P_{\_G44747} 
cmark_r P_{\_G44753}

% Constructing a line c which passes through point B and point P_{\_G44753}
line c B P_{\_G44753} 

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; line b and circle k(M_{a},B) intersect; points H_{b} and M_{a} are not the same
% Determination conditions:  lines c and b are not the same; points M_{a} and C are not the same; points H_{b} and C must be different; points H_{b} and T_{b} are not the same