Construction in GCLC language

dim 120 120

point B 20 40
point M_{a} 65 40
point I 74.37 61.15

color 220 0 0
fontsize 11

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


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


% DET:  points B and M_{a} are not the same
% Constructing a line a which passes through point B and point M_{a}
line a B 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_{\_G22190} which is a foot of the point I on the line a
foot P_{\_G22190} I a 
cmark_r P_{\_G22190}
color 200 200 200
drawline I P_{\_G22190} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G22190}
circle k(I,P_{a}) I P_{\_G22190} 

color 200 200 200
drawcircle k(I,P_{a})
color 0 0 0



% NDG:  point B is outside the circle k(I,P_{a})
% Constructing a point P_{\_G22397} which is a foot of the point I on the line a
foot P_{\_G22397} I a 
cmark_r P_{\_G22397}
color 200 200 200
drawline I P_{\_G22397} 
color 0 0 0

% Constructing a line L_{\_G22400} which passes through point I and point B
line L_{\_G22400} I B 

color 200 200 200
drawline L_{\_G22400}
color 0 0 0


% Constructing a point P_{\_G22403} which is an image of the point P_{\_G22397} in the symmetry to point/line L_{\_G22400}
sim P_{\_G22403} L_{\_G22400} P_{\_G22397} 
cmark_r P_{\_G22403}

% Constructing a line c which passes through point B and point P_{\_G22403}
line c B P_{\_G22403} 

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_{\_G22732} which is a foot of the point I on the line a
foot P_{\_G22732} I a 
cmark_r P_{\_G22732}
color 200 200 200
drawline I P_{\_G22732} 
color 0 0 0

% Constructing a line L_{\_G22735} which passes through point I and point C
line L_{\_G22735} I C 

color 200 200 200
drawline L_{\_G22735}
color 0 0 0


% Constructing a point P_{\_G22738} which is an image of the point P_{\_G22732} in the symmetry to point/line L_{\_G22735}
sim P_{\_G22738} L_{\_G22735} P_{\_G22732} 
cmark_r P_{\_G22738}

% Constructing a line b which passes through point C and point P_{\_G22738}
line b C P_{\_G22738} 

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