Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point H_{a} 80 40
point T_{a} 70.86 40

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_b H_{a}
cmark_b T_{a}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



% NDG:  points H_{a} 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_{a}
circle k(M_{c},A) M_{c} H_{a} 

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



% NDG:  line a and circle k(M_{c},A) intersect% DET:  points H_{a} and B must be different
% Constructing a point P_{\_G55597} which is a foot of the point M_{c} on the line a
foot P_{\_G55597} M_{c} a 
cmark_r P_{\_G55597}
color 200 200 200
drawline M_{c} P_{\_G55597} 
color 0 0 0

% Constructing a point B which is an image of the point H_{a} in the symmetry to point/line P_{\_G55597}
sim B P_{\_G55597} H_{a} 
cmark_b B



% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point T_{a} is not incident to the line c
% Constructing a point P_{\_G55881} which is a foot of the point T_{a} on the line c
foot P_{\_G55881} T_{a} c 
cmark_r P_{\_G55881}
color 200 200 200
drawline T_{a} P_{\_G55881} 
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_{\_G55881}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G55881} 

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_{\_G56272} which is a foot of the point T_{a} on the line c
foot P_{\_G56272} T_{a} c 
cmark_r P_{\_G56272}
color 200 200 200
drawline T_{a} P_{\_G56272} 
color 0 0 0

% Constructing a line L_{\_G56275} which passes through point T_{a} and point A
line L_{\_G56275} T_{a} A 

color 200 200 200
drawline L_{\_G56275}
color 0 0 0


% Constructing a point P_{\_G56278} which is an image of the point P_{\_G56272} in the symmetry to point/line L_{\_G56275}
sim P_{\_G56278} L_{\_G56275} P_{\_G56272} 
cmark_r P_{\_G56278}

% Constructing a line b which passes through point A and point P_{\_G56278}
line b A P_{\_G56278} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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