Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point H_{c} 68.91 84.83
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



% NDG:  line c and circle k(M_{b},C) intersect% DET:  points H_{c} and A must be different
% Constructing a point P_{\_G49579} which is a foot of the point M_{b} on the line c
foot P_{\_G49579} M_{b} c 
cmark_r P_{\_G49579}
color 200 200 200
drawline M_{b} P_{\_G49579} 
color 0 0 0

% Constructing a point A which is an image of the point H_{c} in the symmetry to point/line P_{\_G49579}
sim A P_{\_G49579} H_{c} 
cmark_t A



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point T_{c} is not incident to the line b
% Constructing a point P_{\_G49863} which is a foot of the point T_{c} on the line b
foot P_{\_G49863} T_{c} b 
cmark_r P_{\_G49863}
color 200 200 200
drawline T_{c} P_{\_G49863} 
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_{\_G49863}
circle k(T_{c},foot[T_{c},b]) T_{c} P_{\_G49863} 

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_{\_G50254} which is a foot of the point T_{c} on the line b
foot P_{\_G50254} T_{c} b 
cmark_r P_{\_G50254}
color 200 200 200
drawline T_{c} P_{\_G50254} 
color 0 0 0

% Constructing a line L_{\_G50257} which passes through point T_{c} and point C
line L_{\_G50257} T_{c} C 

color 200 200 200
drawline L_{\_G50257}
color 0 0 0


% Constructing a point P_{\_G50260} which is an image of the point P_{\_G50254} in the symmetry to point/line L_{\_G50257}
sim P_{\_G50260} L_{\_G50257} P_{\_G50254} 
cmark_r P_{\_G50260}

% Constructing a line a which passes through point C and point P_{\_G50260}
line a C P_{\_G50260} 

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