Construction in GCLC language

dim 120 120

point A 80 95
point M_{b} 95 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

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


% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  point I is not incident to the line b
% Constructing a point P_{\_G11811} which is a foot of the point I on the line b
foot P_{\_G11811} I b 
cmark_r P_{\_G11811}
color 200 200 200
drawline I P_{\_G11811} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G11811}
circle k(I,P_{a}) I P_{\_G11811} 

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_{\_G12018} which is a foot of the point I on the line b
foot P_{\_G12018} I b 
cmark_r P_{\_G12018}
color 200 200 200
drawline I P_{\_G12018} 
color 0 0 0

% Constructing a line L_{\_G12021} which passes through point I and point A
line L_{\_G12021} I A 

color 200 200 200
drawline L_{\_G12021}
color 0 0 0


% Constructing a point P_{\_G12024} which is an image of the point P_{\_G12018} in the symmetry to point/line L_{\_G12021}
sim P_{\_G12024} L_{\_G12021} P_{\_G12018} 
cmark_r P_{\_G12024}

% Constructing a line c which passes through point A and point P_{\_G12024}
line c A P_{\_G12024} 

color 200 200 200
drawline c
color 0 0 0



% NDG:  point C is outside the circle k(I,P_{a})
% Constructing a point P_{\_G12353} which is a foot of the point I on the line b
foot P_{\_G12353} I b 
cmark_r P_{\_G12353}
color 200 200 200
drawline I P_{\_G12353} 
color 0 0 0

% Constructing a line L_{\_G12356} which passes through point I and point C
line L_{\_G12356} I C 

color 200 200 200
drawline L_{\_G12356}
color 0 0 0


% Constructing a point P_{\_G12359} which is an image of the point P_{\_G12353} in the symmetry to point/line L_{\_G12356}
sim P_{\_G12359} L_{\_G12356} P_{\_G12353} 
cmark_r P_{\_G12359}

% Constructing a line a which passes through point C and point P_{\_G12359}
line a C P_{\_G12359} 

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