Construction in GCLC language

dim 120 120

point A 80 95
point H_{b} 89.36 77.83
point I 74.37 61.15

color 220 0 0
fontsize 11

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

% DET:  points A and H_{b} are not the same
% Constructing a line b which passes through point A and point H_{b}
line b A 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_{\_G19298} which is a foot of the point I on the line b
foot P_{\_G19298} I b 
cmark_r P_{\_G19298}
color 200 200 200
drawline I P_{\_G19298} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G19298}
circle k(I,P_{a}) I P_{\_G19298} 

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_{\_G19505} which is a foot of the point I on the line b
foot P_{\_G19505} I b 
cmark_r P_{\_G19505}
color 200 200 200
drawline I P_{\_G19505} 
color 0 0 0

% Constructing a line L_{\_G19508} which passes through point I and point A
line L_{\_G19508} I A 

color 200 200 200
drawline L_{\_G19508}
color 0 0 0


% Constructing a point P_{\_G19511} which is an image of the point P_{\_G19505} in the symmetry to point/line L_{\_G19508}
sim P_{\_G19511} L_{\_G19508} P_{\_G19505} 
cmark_r P_{\_G19511}

% Constructing a line c which passes through point A and point P_{\_G19511}
line c A P_{\_G19511} 

color 200 200 200
drawline c
color 0 0 0



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


% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G19897} which is a foot of the point I on the line c
foot P_{\_G19897} I c 
cmark_r P_{\_G19897}
color 200 200 200
drawline I P_{\_G19897} 
color 0 0 0

% Constructing a line L_{\_G19900} which passes through point I and point B
line L_{\_G19900} I B 

color 200 200 200
drawline L_{\_G19900}
color 0 0 0


% Constructing a point P_{\_G19903} which is an image of the point P_{\_G19897} in the symmetry to point/line L_{\_G19900}
sim P_{\_G19903} L_{\_G19900} P_{\_G19897} 
cmark_r P_{\_G19903}

% Constructing a line a which passes through point B and point P_{\_G19903}
line a B P_{\_G19903} 

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 h_{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 h_{b} are not the same; points A and H_{b} are not the same