Construction in GCLC language

dim 120 120

point A 80 95
point B 20 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_b B
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G6065} which is a foot of the point I on the line c
foot P_{\_G6065} I c 
cmark_r P_{\_G6065}
color 200 200 200
drawline I P_{\_G6065} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G6065}
circle k(I,P_{a}) I P_{\_G6065} 

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



% NDG:  point A is outside the circle k(I,P_{a})
% Constructing a point P_{\_G6272} which is a foot of the point I on the line c
foot P_{\_G6272} I c 
cmark_r P_{\_G6272}
color 200 200 200
drawline I P_{\_G6272} 
color 0 0 0

% Constructing a line L_{\_G6275} which passes through point I and point A
line L_{\_G6275} I A 

color 200 200 200
drawline L_{\_G6275}
color 0 0 0


% Constructing a point P_{\_G6278} which is an image of the point P_{\_G6272} in the symmetry to point/line L_{\_G6275}
sim P_{\_G6278} L_{\_G6275} P_{\_G6272} 
cmark_r P_{\_G6278}

% Constructing a line b which passes through point A and point P_{\_G6278}
line b A P_{\_G6278} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G6607} which is a foot of the point I on the line c
foot P_{\_G6607} I c 
cmark_r P_{\_G6607}
color 200 200 200
drawline I P_{\_G6607} 
color 0 0 0

% Constructing a line L_{\_G6610} which passes through point I and point B
line L_{\_G6610} I B 

color 200 200 200
drawline L_{\_G6610}
color 0 0 0


% Constructing a point P_{\_G6613} which is an image of the point P_{\_G6607} in the symmetry to point/line L_{\_G6610}
sim P_{\_G6613} L_{\_G6610} P_{\_G6607} 
cmark_r P_{\_G6613}

% Constructing a line a which passes through point B and point P_{\_G6613}
line a B P_{\_G6613} 

color 200 200 200
drawline a
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 B is outside the circle k(I,P_{a}); point A is outside the circle k(I,P_{a}); point I is not incident to the line c
% Determination conditions:  lines b and a are not the same; points A and B are not the same