Construction in GCLC language

dim 120 120

point B 20 40
point T_{c} 55.38 72.43
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b B
cmark_lt T_{c}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline s_{c}
color 0 0 0



% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G40399} which is a foot of the point I on the line c
foot P_{\_G40399} I c 
cmark_r P_{\_G40399}
color 200 200 200
drawline I P_{\_G40399} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G40399}
circle k(I,P_{a}) I P_{\_G40399} 

color 200 200 200
drawcircle k(I,P_{a})
color 0 0 0



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G40606} which is a foot of the point I on the line c
foot P_{\_G40606} I c 
cmark_r P_{\_G40606}
color 200 200 200
drawline I P_{\_G40606} 
color 0 0 0

% Constructing a line L_{\_G40609} which passes through point I and point B
line L_{\_G40609} I B 

color 200 200 200
drawline L_{\_G40609}
color 0 0 0


% Constructing a point P_{\_G40612} which is an image of the point P_{\_G40606} in the symmetry to point/line L_{\_G40609}
sim P_{\_G40612} L_{\_G40609} P_{\_G40606} 
cmark_r P_{\_G40612}

% Constructing a line a which passes through point B and point P_{\_G40612}
line a B P_{\_G40612} 

color 200 200 200
drawline a
color 0 0 0



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


% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G40998} which is a foot of the point I on the line a
foot P_{\_G40998} I a 
cmark_r P_{\_G40998}
color 200 200 200
drawline I P_{\_G40998} 
color 0 0 0

% Constructing a line L_{\_G41001} which passes through point I and point C
line L_{\_G41001} I C 

color 200 200 200
drawline L_{\_G41001}
color 0 0 0


% Constructing a point P_{\_G41004} which is an image of the point P_{\_G40998} in the symmetry to point/line L_{\_G41001}
sim P_{\_G41004} L_{\_G41001} P_{\_G40998} 
cmark_r P_{\_G41004}

% Constructing a line b which passes through point C and point P_{\_G41004}
line b C P_{\_G41004} 

color 200 200 200
drawline b
color 0 0 0



% 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; point C is outside the circle k(I,P_{a}); lines a and s_{c} are not parallel; point B is outside the circle k(I,P_{a}); point I is not incident to the line c
% Determination conditions:  lines b and c are not the same; lines a and s_{c} are not the same; points T_{c} and I are not the same; points B and T_{c} are not the same