Construction in GCLC language

dim 120 120

point C 110 40
point T_{a} 70.86 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b C
cmark_b T_{a}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline a
color 0 0 0



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

color 200 200 200
drawline s_{a}
color 0 0 0



% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G56460} which is a foot of the point I on the line a
foot P_{\_G56460} I a 
cmark_r P_{\_G56460}
color 200 200 200
drawline I P_{\_G56460} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G56460}
circle k(I,P_{a}) I P_{\_G56460} 

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



% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G56667} which is a foot of the point I on the line a
foot P_{\_G56667} I a 
cmark_r P_{\_G56667}
color 200 200 200
drawline I P_{\_G56667} 
color 0 0 0

% Constructing a line L_{\_G56670} which passes through point I and point C
line L_{\_G56670} I C 

color 200 200 200
drawline L_{\_G56670}
color 0 0 0


% Constructing a point P_{\_G56673} which is an image of the point P_{\_G56667} in the symmetry to point/line L_{\_G56670}
sim P_{\_G56673} L_{\_G56670} P_{\_G56667} 
cmark_r P_{\_G56673}

% Constructing a line b which passes through point C and point P_{\_G56673}
line b C P_{\_G56673} 

color 200 200 200
drawline b
color 0 0 0



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


% NDG:  point A is outside the circle k(I,P_{a})
% Constructing a point P_{\_G57059} which is a foot of the point I on the line b
foot P_{\_G57059} I b 
cmark_r P_{\_G57059}
color 200 200 200
drawline I P_{\_G57059} 
color 0 0 0

% Constructing a line L_{\_G57062} which passes through point I and point A
line L_{\_G57062} I A 

color 200 200 200
drawline L_{\_G57062}
color 0 0 0


% Constructing a point P_{\_G57065} which is an image of the point P_{\_G57059} in the symmetry to point/line L_{\_G57062}
sim P_{\_G57065} L_{\_G57062} P_{\_G57059} 
cmark_r P_{\_G57065}

% Constructing a line c which passes through point A and point P_{\_G57065}
line c A P_{\_G57065} 

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