Construction in GCLC language

dim 120 120

point C 110 40
point H_{b} 89.36 77.83
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b C
cmark_rt H_{b}
cmark_b I
color 0 0 0
fontsize 10

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

color 200 200 200
drawline b
color 0 0 0




% Constructing a line h_{b} which is perpendicular to line b and which passes through point H_{b}
perp h_{b} H_{b} b 

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G45701} which is a foot of the point I on the line b
foot P_{\_G45701} I b 
cmark_r P_{\_G45701}
color 200 200 200
drawline I P_{\_G45701} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G45701}
circle k(I,P_{a}) I P_{\_G45701} 

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_{\_G45908} which is a foot of the point I on the line b
foot P_{\_G45908} I b 
cmark_r P_{\_G45908}
color 200 200 200
drawline I P_{\_G45908} 
color 0 0 0

% Constructing a line L_{\_G45911} which passes through point I and point C
line L_{\_G45911} I C 

color 200 200 200
drawline L_{\_G45911}
color 0 0 0


% Constructing a point P_{\_G45914} which is an image of the point P_{\_G45908} in the symmetry to point/line L_{\_G45911}
sim P_{\_G45914} L_{\_G45911} P_{\_G45908} 
cmark_r P_{\_G45914}

% Constructing a line a which passes through point C and point P_{\_G45914}
line a C P_{\_G45914} 

color 200 200 200
drawline a
color 0 0 0



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


% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G46300} which is a foot of the point I on the line a
foot P_{\_G46300} I a 
cmark_r P_{\_G46300}
color 200 200 200
drawline I P_{\_G46300} 
color 0 0 0

% Constructing a line L_{\_G46303} which passes through point I and point B
line L_{\_G46303} I B 

color 200 200 200
drawline L_{\_G46303}
color 0 0 0


% Constructing a point P_{\_G46306} which is an image of the point P_{\_G46300} in the symmetry to point/line L_{\_G46303}
sim P_{\_G46306} L_{\_G46303} P_{\_G46300} 
cmark_r P_{\_G46306}

% Constructing a line c which passes through point B and point P_{\_G46306}
line c B P_{\_G46306} 

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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