Construction in GCLC language

dim 120 120

point C 110 40
point T_{a} 70.86 40
point T_{c} 55.38 72.43

color 220 0 0
fontsize 11

cmark_b C
cmark_b T_{a}
cmark_lt T_{c}
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point T_{c} is not incident to the line a
% Constructing a point P_{\_G60991} which is a foot of the point T_{c} on the line a
foot P_{\_G60991} T_{c} a 
cmark_r P_{\_G60991}
color 200 200 200
drawline T_{c} P_{\_G60991} 
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_{\_G60991}
circle k(T_{c},foot[T_{c},b]) T_{c} P_{\_G60991} 

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_{\_G61382} which is a foot of the point T_{c} on the line a
foot P_{\_G61382} T_{c} a 
cmark_r P_{\_G61382}
color 200 200 200
drawline T_{c} P_{\_G61382} 
color 0 0 0

% Constructing a line L_{\_G61385} which passes through point T_{c} and point C
line L_{\_G61385} T_{c} C 

color 200 200 200
drawline L_{\_G61385}
color 0 0 0


% Constructing a point P_{\_G61388} which is an image of the point P_{\_G61382} in the symmetry to point/line L_{\_G61385}
sim P_{\_G61388} L_{\_G61385} P_{\_G61382} 
cmark_r P_{\_G61388}

% Constructing a line b which passes through point C and point P_{\_G61388}
line b C P_{\_G61388} 

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_{\_G61669} which is a foot of the point T_{a} on the line b
foot P_{\_G61669} T_{a} b 
cmark_r P_{\_G61669}
color 200 200 200
drawline T_{a} P_{\_G61669} 
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_{\_G61669}
circle k(T_{a},foot[T_{a},c]) T_{a} P_{\_G61669} 

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



% NDG:  point T_{c} is outside the circle k(T_{a},foot[T_{a},c])
% Constructing midpoint P_{\_G62087} of the segment T_{c}T_{a}
midpoint P_{\_G62087} T_{c} T_{a} 
cmark_r P_{\_G62087}

% Constructing a circle C_{\_G62090} whose center is at point P_{\_G62087} and which passes through point T_{c}
circle C_{\_G62090} P_{\_G62087} T_{c} 

color 200 200 200
drawcircle C_{\_G62090}
color 0 0 0


% Constructing points P_{\_G62093} and P_{\_G62096} which are in intersection of C_{\_G62090} and k(T_{a},foot[T_{a},c])
intersec2 P_{\_G62093} P_{\_G62096} C_{\_G62090} k(T_{a},foot[T_{a},c]) 
cmark_r P_{\_G62093}
cmark_r P_{\_G62096}

% Constructing a line c1 which passes through point T_{c} and point P_{\_G62093}
line c1 T_{c} P_{\_G62093} 

color 200 200 200
drawline c1
color 0 0 0


% Constructing a line c which passes through point T_{c} and point P_{\_G62096}
line c T_{c} P_{\_G62096} 

color 200 200 200
drawline c
color 0 0 0



% 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


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



drawsegment A B
drawsegment A C
drawsegment B C

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