Construction in GCLC language

dim 120 120

point B 20 40
point M_{c} 50 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b B
cmark_lt M_{c}
cmark_b I
color 0 0 0
fontsize 10


% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0


% DET:  points B and M_{c} are not the same
% Constructing a line c which passes through point B and point M_{c}
line c B 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_{\_G27318} which is a foot of the point I on the line c
foot P_{\_G27318} I c 
cmark_r P_{\_G27318}
color 200 200 200
drawline I P_{\_G27318} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G27318}
circle k(I,P_{a}) I P_{\_G27318} 

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_{\_G27525} which is a foot of the point I on the line c
foot P_{\_G27525} I c 
cmark_r P_{\_G27525}
color 200 200 200
drawline I P_{\_G27525} 
color 0 0 0

% Constructing a line L_{\_G27528} which passes through point I and point B
line L_{\_G27528} I B 

color 200 200 200
drawline L_{\_G27528}
color 0 0 0


% Constructing a point P_{\_G27531} which is an image of the point P_{\_G27525} in the symmetry to point/line L_{\_G27528}
sim P_{\_G27531} L_{\_G27528} P_{\_G27525} 
cmark_r P_{\_G27531}

% Constructing a line a which passes through point B and point P_{\_G27531}
line a B P_{\_G27531} 

color 200 200 200
drawline a
color 0 0 0



% NDG:  point A is outside the circle k(I,P_{a})
% Constructing a point P_{\_G27860} which is a foot of the point I on the line c
foot P_{\_G27860} I c 
cmark_r P_{\_G27860}
color 200 200 200
drawline I P_{\_G27860} 
color 0 0 0

% Constructing a line L_{\_G27863} which passes through point I and point A
line L_{\_G27863} I A 

color 200 200 200
drawline L_{\_G27863}
color 0 0 0


% Constructing a point P_{\_G27866} which is an image of the point P_{\_G27860} in the symmetry to point/line L_{\_G27863}
sim P_{\_G27866} L_{\_G27863} P_{\_G27860} 
cmark_r P_{\_G27866}

% Constructing a line b which passes through point A and point P_{\_G27866}
line b A P_{\_G27866} 

color 200 200 200
drawline b
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 A 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 c
% Determination conditions:  lines a and b are not the same; points B and M_{c} are not the same