Construction in GCLC language

dim 120 120

point A 80 95
point C 110 40
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G4438} which is a foot of the point I on the line b
foot P_{\_G4438} I b 
cmark_r P_{\_G4438}
color 200 200 200
drawline I P_{\_G4438} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G4438}
circle k(I,P_{a}) I P_{\_G4438} 

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_{\_G4645} which is a foot of the point I on the line b
foot P_{\_G4645} I b 
cmark_r P_{\_G4645}
color 200 200 200
drawline I P_{\_G4645} 
color 0 0 0

% Constructing a line L_{\_G4648} which passes through point I and point A
line L_{\_G4648} I A 

color 200 200 200
drawline L_{\_G4648}
color 0 0 0


% Constructing a point P_{\_G4651} which is an image of the point P_{\_G4645} in the symmetry to point/line L_{\_G4648}
sim P_{\_G4651} L_{\_G4648} P_{\_G4645} 
cmark_r P_{\_G4651}

% Constructing a line c which passes through point A and point P_{\_G4651}
line c A P_{\_G4651} 

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_{\_G4980} which is a foot of the point I on the line b
foot P_{\_G4980} I b 
cmark_r P_{\_G4980}
color 200 200 200
drawline I P_{\_G4980} 
color 0 0 0

% Constructing a line L_{\_G4983} which passes through point I and point C
line L_{\_G4983} I C 

color 200 200 200
drawline L_{\_G4983}
color 0 0 0


% Constructing a point P_{\_G4986} which is an image of the point P_{\_G4980} in the symmetry to point/line L_{\_G4983}
sim P_{\_G4986} L_{\_G4983} P_{\_G4980} 
cmark_r P_{\_G4986}

% Constructing a line a which passes through point C and point P_{\_G4986}
line a C P_{\_G4986} 

color 200 200 200
drawline a
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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines c and a are not parallel; point C 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 b
% Determination conditions:  lines c and a are not the same; points A and C are not the same