Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point H_{b} 89.36 77.83
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_lt M_{c}
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_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point H_{b}
circle k(M_{c},A) M_{c} H_{b} 

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  line b and circle k(M_{c},A) intersect% DET:  points H_{b} and A must be different
% Constructing a point P_{\_G57797} which is a foot of the point M_{c} on the line b
foot P_{\_G57797} M_{c} b 
cmark_r P_{\_G57797}
color 200 200 200
drawline M_{c} P_{\_G57797} 
color 0 0 0

% Constructing a point A which is an image of the point H_{b} in the symmetry to point/line P_{\_G57797}
sim A P_{\_G57797} H_{b} 
cmark_t A



% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point T_{b} is not incident to the line c
% Constructing a point P_{\_G58081} which is a foot of the point T_{b} on the line c
foot P_{\_G58081} T_{b} c 
cmark_r P_{\_G58081}
color 200 200 200
drawline T_{b} P_{\_G58081} 
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_{\_G58081}
circle k(T_{b},foot[T_{b},c]) T_{b} P_{\_G58081} 

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_{\_G58472} which is a foot of the point T_{b} on the line c
foot P_{\_G58472} T_{b} c 
cmark_r P_{\_G58472}
color 200 200 200
drawline T_{b} P_{\_G58472} 
color 0 0 0

% Constructing a line L_{\_G58475} which passes through point T_{b} and point B
line L_{\_G58475} T_{b} B 

color 200 200 200
drawline L_{\_G58475}
color 0 0 0


% Constructing a point P_{\_G58478} which is an image of the point P_{\_G58472} in the symmetry to point/line L_{\_G58475}
sim P_{\_G58478} L_{\_G58475} P_{\_G58472} 
cmark_r P_{\_G58478}

% Constructing a line a which passes through point B and point P_{\_G58478}
line a B P_{\_G58478} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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