Construction in GCLC language

dim 120 120

point A 80 95
point T_{a} 70.86 40
point T_{b} 94.25 68.88

color 220 0 0
fontsize 11

cmark_t A
cmark_b T_{a}
cmark_rt T_{b}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point T_{a} is not incident to the line b
% Constructing a point P_{\_G18955} which is a foot of the point T_{a} on the line b
foot P_{\_G18955} T_{a} b 
cmark_r P_{\_G18955}
color 200 200 200
drawline T_{a} P_{\_G18955} 
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_{\_G18955}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G18955} 

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_{\_G19346} which is a foot of the point T_{a} on the line b
foot P_{\_G19346} T_{a} b 
cmark_r P_{\_G19346}
color 200 200 200
drawline T_{a} P_{\_G19346} 
color 0 0 0

% Constructing a line L_{\_G19349} which passes through point T_{a} and point A
line L_{\_G19349} T_{a} A 

color 200 200 200
drawline L_{\_G19349}
color 0 0 0


% Constructing a point P_{\_G19352} which is an image of the point P_{\_G19346} in the symmetry to point/line L_{\_G19349}
sim P_{\_G19352} L_{\_G19349} P_{\_G19346} 
cmark_r P_{\_G19352}

% Constructing a line c which passes through point A and point P_{\_G19352}
line c A P_{\_G19352} 

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_{\_G19633} which is a foot of the point T_{b} on the line c
foot P_{\_G19633} T_{b} c 
cmark_r P_{\_G19633}
color 200 200 200
drawline T_{b} P_{\_G19633} 
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_{\_G19633}
circle k(T_{b},foot[T_{b},c]) T_{b} P_{\_G19633} 

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



% NDG:  point T_{a} is outside the circle k(T_{b},foot[T_{b},c])
% Constructing midpoint P_{\_G20051} of the segment T_{a}T_{b}
midpoint P_{\_G20051} T_{a} T_{b} 
cmark_r P_{\_G20051}

% Constructing a circle C_{\_G20054} whose center is at point P_{\_G20051} and which passes through point T_{a}
circle C_{\_G20054} P_{\_G20051} T_{a} 

color 200 200 200
drawcircle C_{\_G20054}
color 0 0 0


% Constructing points P_{\_G20057} and P_{\_G20060} which are in intersection of C_{\_G20054} and k(T_{b},foot[T_{b},c])
intersec2 P_{\_G20057} P_{\_G20060} C_{\_G20054} k(T_{b},foot[T_{b},c]) 
cmark_r P_{\_G20057}
cmark_r P_{\_G20060}

% Constructing a line a1 which passes through point T_{a} and point P_{\_G20057}
line a1 T_{a} P_{\_G20057} 

color 200 200 200
drawline a1
color 0 0 0


% Constructing a line a which passes through point T_{a} and point P_{\_G20060}
line a T_{a} P_{\_G20060} 

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


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



drawsegment A B
drawsegment A C
drawsegment B C

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