Construction in GCLC language

dim 120 120

point B 20 40
point C 110 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b B
cmark_b C
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G27536} which is a foot of the point I on the line a
foot P_{\_G27536} I a 
cmark_r P_{\_G27536}
color 200 200 200
drawline I P_{\_G27536} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G27536}
circle k(I,P_{a}) I P_{\_G27536} 

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_{\_G27743} which is a foot of the point I on the line a
foot P_{\_G27743} I a 
cmark_r P_{\_G27743}
color 200 200 200
drawline I P_{\_G27743} 
color 0 0 0

% Constructing a line L_{\_G27746} which passes through point I and point B
line L_{\_G27746} I B 

color 200 200 200
drawline L_{\_G27746}
color 0 0 0


% Constructing a point P_{\_G27749} which is an image of the point P_{\_G27743} in the symmetry to point/line L_{\_G27746}
sim P_{\_G27749} L_{\_G27746} P_{\_G27743} 
cmark_r P_{\_G27749}

% Constructing a line c which passes through point B and point P_{\_G27749}
line c B P_{\_G27749} 

color 200 200 200
drawline c
color 0 0 0



% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G28078} which is a foot of the point I on the line a
foot P_{\_G28078} I a 
cmark_r P_{\_G28078}
color 200 200 200
drawline I P_{\_G28078} 
color 0 0 0

% Constructing a line L_{\_G28081} which passes through point I and point C
line L_{\_G28081} I C 

color 200 200 200
drawline L_{\_G28081}
color 0 0 0


% Constructing a point P_{\_G28084} which is an image of the point P_{\_G28078} in the symmetry to point/line L_{\_G28081}
sim P_{\_G28084} L_{\_G28081} P_{\_G28078} 
cmark_r P_{\_G28084}

% Constructing a line b which passes through point C and point P_{\_G28084}
line b C P_{\_G28084} 

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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