Construction in GCLC language

dim 120 120

point A 80 95
point T_{b} 94.25 68.88
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_rt T_{b}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline s_{b}
color 0 0 0



% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G26554} which is a foot of the point I on the line b
foot P_{\_G26554} I b 
cmark_r P_{\_G26554}
color 200 200 200
drawline I P_{\_G26554} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G26554}
circle k(I,P_{a}) I P_{\_G26554} 

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_{\_G26761} which is a foot of the point I on the line b
foot P_{\_G26761} I b 
cmark_r P_{\_G26761}
color 200 200 200
drawline I P_{\_G26761} 
color 0 0 0

% Constructing a line L_{\_G26764} which passes through point I and point A
line L_{\_G26764} I A 

color 200 200 200
drawline L_{\_G26764}
color 0 0 0


% Constructing a point P_{\_G26767} which is an image of the point P_{\_G26761} in the symmetry to point/line L_{\_G26764}
sim P_{\_G26767} L_{\_G26764} P_{\_G26761} 
cmark_r P_{\_G26767}

% Constructing a line c which passes through point A and point P_{\_G26767}
line c A P_{\_G26767} 

color 200 200 200
drawline c
color 0 0 0



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


% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G27153} which is a foot of the point I on the line c
foot P_{\_G27153} I c 
cmark_r P_{\_G27153}
color 200 200 200
drawline I P_{\_G27153} 
color 0 0 0

% Constructing a line L_{\_G27156} which passes through point I and point B
line L_{\_G27156} I B 

color 200 200 200
drawline L_{\_G27156}
color 0 0 0


% Constructing a point P_{\_G27159} which is an image of the point P_{\_G27153} in the symmetry to point/line L_{\_G27156}
sim P_{\_G27159} L_{\_G27156} P_{\_G27153} 
cmark_r P_{\_G27159}

% Constructing a line a which passes through point B and point P_{\_G27159}
line a B P_{\_G27159} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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