Construction in GCLC language

dim 120 120

point C 110 40
point M_{a} 65 40
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b C
cmark_b M_{a}
cmark_b I
color 0 0 0
fontsize 10


% Constructing a point B such that CB/CM_{a}=2
towards B C M_{a} 2 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0


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

color 200 200 200
drawline a
color 0 0 0



% NDG:  point I is not incident to the line a
% Constructing a point P_{\_G41931} which is a foot of the point I on the line a
foot P_{\_G41931} I a 
cmark_r P_{\_G41931}
color 200 200 200
drawline I P_{\_G41931} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G41931}
circle k(I,P_{a}) I P_{\_G41931} 

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_{\_G42138} which is a foot of the point I on the line a
foot P_{\_G42138} I a 
cmark_r P_{\_G42138}
color 200 200 200
drawline I P_{\_G42138} 
color 0 0 0

% Constructing a line L_{\_G42141} which passes through point I and point C
line L_{\_G42141} I C 

color 200 200 200
drawline L_{\_G42141}
color 0 0 0


% Constructing a point P_{\_G42144} which is an image of the point P_{\_G42138} in the symmetry to point/line L_{\_G42141}
sim P_{\_G42144} L_{\_G42141} P_{\_G42138} 
cmark_r P_{\_G42144}

% Constructing a line b which passes through point C and point P_{\_G42144}
line b C P_{\_G42144} 

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_{\_G42473} which is a foot of the point I on the line a
foot P_{\_G42473} I a 
cmark_r P_{\_G42473}
color 200 200 200
drawline I P_{\_G42473} 
color 0 0 0

% Constructing a line L_{\_G42476} which passes through point I and point B
line L_{\_G42476} I B 

color 200 200 200
drawline L_{\_G42476}
color 0 0 0


% Constructing a point P_{\_G42479} which is an image of the point P_{\_G42473} in the symmetry to point/line L_{\_G42476}
sim P_{\_G42479} L_{\_G42476} P_{\_G42473} 
cmark_r P_{\_G42479}

% Constructing a line c which passes through point B and point P_{\_G42479}
line c B P_{\_G42479} 

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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