Construction in GCLC language

dim 120 120

point C 110 40
point M_{b} 95 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b C
cmark_rt M_{b}
cmark_b I
color 0 0 0
fontsize 10


% Constructing a point A such that CA/CM_{b}=2
towards A C M_{b} 2 
cmark_t A
color 200 200 200
drawsegment C A 
color 0 0 0


% DET:  points C and M_{b} are not the same
% Constructing a line b which passes through point C and point M_{b}
line b C 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_{\_G48074} which is a foot of the point I on the line b
foot P_{\_G48074} I b 
cmark_r P_{\_G48074}
color 200 200 200
drawline I P_{\_G48074} 
color 0 0 0

% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{\_G48074}
circle k(I,P_{a}) I P_{\_G48074} 

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_{\_G48281} which is a foot of the point I on the line b
foot P_{\_G48281} I b 
cmark_r P_{\_G48281}
color 200 200 200
drawline I P_{\_G48281} 
color 0 0 0

% Constructing a line L_{\_G48284} which passes through point I and point C
line L_{\_G48284} I C 

color 200 200 200
drawline L_{\_G48284}
color 0 0 0


% Constructing a point P_{\_G48287} which is an image of the point P_{\_G48281} in the symmetry to point/line L_{\_G48284}
sim P_{\_G48287} L_{\_G48284} P_{\_G48281} 
cmark_r P_{\_G48287}

% Constructing a line a which passes through point C and point P_{\_G48287}
line a C P_{\_G48287} 

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_{\_G48616} which is a foot of the point I on the line b
foot P_{\_G48616} I b 
cmark_r P_{\_G48616}
color 200 200 200
drawline I P_{\_G48616} 
color 0 0 0

% Constructing a line L_{\_G48619} which passes through point I and point A
line L_{\_G48619} I A 

color 200 200 200
drawline L_{\_G48619}
color 0 0 0


% Constructing a point P_{\_G48622} which is an image of the point P_{\_G48616} in the symmetry to point/line L_{\_G48619}
sim P_{\_G48622} L_{\_G48619} P_{\_G48616} 
cmark_r P_{\_G48622}

% Constructing a line c which passes through point A and point P_{\_G48622}
line c A P_{\_G48622} 

color 200 200 200
drawline c
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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