Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point T_{c} 55.38 72.43
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_lt T_{c}
cmark_b I
color 0 0 0
fontsize 10

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




% Constructing a line m_{c} which is perpendicular to line c and which passes through point M_{c}
perp m_{c} M_{c} c 

color 200 200 200
drawline m_{c}
color 0 0 0



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


% NDG:  points I and N_{c} are not the same
% Constructing a circle k(N_{c},B) whose center is at point N_{c} and which passes through point I
circle k(N_{c},B) N_{c} I 

color 200 200 200
drawcircle k(N_{c},B)
color 0 0 0



% NDG:  line c and circle k(N_{c},B) intersect
% Constructing points B and A which are in intersection of k(N_{c},B) and c
intersec2 B A k(N_{c},B) c 
cmark_b B
cmark_t A


% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G65427} which is a foot of the point I on the line c
foot P_{\_G65427} I c 
cmark_r P_{\_G65427}
color 200 200 200
drawline I P_{\_G65427} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G65427}
circle k(I,P_{a}) I P_{\_G65427} 

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



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G65634} which is a foot of the point I on the line c
foot P_{\_G65634} I c 
cmark_r P_{\_G65634}
color 200 200 200
drawline I P_{\_G65634} 
color 0 0 0

% Constructing a line L_{\_G65637} which passes through point I and point B
line L_{\_G65637} I B 

color 200 200 200
drawline L_{\_G65637}
color 0 0 0


% Constructing a point P_{\_G65640} which is an image of the point P_{\_G65634} in the symmetry to point/line L_{\_G65637}
sim P_{\_G65640} L_{\_G65637} P_{\_G65634} 
cmark_r P_{\_G65640}

% Constructing a line a which passes through point B and point P_{\_G65640}
line a B P_{\_G65640} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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