Construction in GCLC language

dim 120 120

point A 80 95
point T_{c} 55.38 72.43
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_t A
cmark_lt T_{c}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline s_{c}
color 0 0 0



% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G12114} which is a foot of the point I on the line c
foot P_{\_G12114} I c 
cmark_r P_{\_G12114}
color 200 200 200
drawline I P_{\_G12114} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G12114}
circle k(I,P_{a}) I P_{\_G12114} 

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_{\_G12321} which is a foot of the point I on the line c
foot P_{\_G12321} I c 
cmark_r P_{\_G12321}
color 200 200 200
drawline I P_{\_G12321} 
color 0 0 0

% Constructing a line L_{\_G12324} which passes through point I and point A
line L_{\_G12324} I A 

color 200 200 200
drawline L_{\_G12324}
color 0 0 0


% Constructing a point P_{\_G12327} which is an image of the point P_{\_G12321} in the symmetry to point/line L_{\_G12324}
sim P_{\_G12327} L_{\_G12324} P_{\_G12321} 
cmark_r P_{\_G12327}

% Constructing a line b which passes through point A and point P_{\_G12327}
line b A P_{\_G12327} 

color 200 200 200
drawline b
color 0 0 0



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


% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G12713} which is a foot of the point I on the line b
foot P_{\_G12713} I b 
cmark_r P_{\_G12713}
color 200 200 200
drawline I P_{\_G12713} 
color 0 0 0

% Constructing a line L_{\_G12716} which passes through point I and point C
line L_{\_G12716} I C 

color 200 200 200
drawline L_{\_G12716}
color 0 0 0


% Constructing a point P_{\_G12719} which is an image of the point P_{\_G12713} in the symmetry to point/line L_{\_G12716}
sim P_{\_G12719} L_{\_G12716} P_{\_G12713} 
cmark_r P_{\_G12719}

% Constructing a line a which passes through point C and point P_{\_G12719}
line a C P_{\_G12719} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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