Construction in GCLC language

dim 120 120

point A 80 95
point M_{c} 50 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

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


% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



% NDG:  point I is not incident to the line c
% Constructing a point P_{\_G11441} which is a foot of the point I on the line c
foot P_{\_G11441} I c 
cmark_r P_{\_G11441}
color 200 200 200
drawline I P_{\_G11441} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G11441}
circle k(I,P_{a}) I P_{\_G11441} 

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_{\_G11648} which is a foot of the point I on the line c
foot P_{\_G11648} I c 
cmark_r P_{\_G11648}
color 200 200 200
drawline I P_{\_G11648} 
color 0 0 0

% Constructing a line L_{\_G11651} which passes through point I and point A
line L_{\_G11651} I A 

color 200 200 200
drawline L_{\_G11651}
color 0 0 0


% Constructing a point P_{\_G11654} which is an image of the point P_{\_G11648} in the symmetry to point/line L_{\_G11651}
sim P_{\_G11654} L_{\_G11651} P_{\_G11648} 
cmark_r P_{\_G11654}

% Constructing a line b which passes through point A and point P_{\_G11654}
line b A P_{\_G11654} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G11983} which is a foot of the point I on the line c
foot P_{\_G11983} I c 
cmark_r P_{\_G11983}
color 200 200 200
drawline I P_{\_G11983} 
color 0 0 0

% Constructing a line L_{\_G11986} which passes through point I and point B
line L_{\_G11986} I B 

color 200 200 200
drawline L_{\_G11986}
color 0 0 0


% Constructing a point P_{\_G11989} which is an image of the point P_{\_G11983} in the symmetry to point/line L_{\_G11986}
sim P_{\_G11989} L_{\_G11986} P_{\_G11983} 
cmark_r P_{\_G11989}

% Constructing a line a which passes through point B and point P_{\_G11989}
line a B P_{\_G11989} 

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines b and a are not parallel; point B 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 c
% Determination conditions:  lines b and a are not the same; points A and M_{c} are not the same