Construction in GCLC language

dim 120 120

point C 110 40
point M_{c} 50 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline IM_{c}
color 0 0 0



% NDG:  points I and M_{c} are not the same
% Constructing midpoint P_{\_G43601} of the segment IM_{c}
midpoint P_{\_G43601} I M_{c} 
cmark_r P_{\_G43601}

% Constructing a circle k_over(I,M_{c}) whose center is at point P_{\_G43601} and which passes through point I
circle k_over(I,M_{c}) P_{\_G43601} I 

color 200 200 200
drawcircle k_over(I,M_{c})
color 0 0 0




% Constructing a line CP`_{c} which contains the point C and is parallel to the line IM_{c}
parallel CP`_{c} C IM_{c} 

color 200 200 200
drawline CP`_{c}
color 0 0 0




% Constructing a point P_{\_G43902} such that M_{c}P_{\_G43902}/M_{c}C=-1
towards P_{\_G43902} M_{c} C -1 
cmark_r P_{\_G43902}
color 200 200 200
drawsegment C P_{\_G43902} 
color 0 0 0

% Constructing a line h_{M_{c},-1/1}(CP`_{c}) which contains the point P_{\_G43902} and is parallel to the line CP`_{c}
parallel h_{M_{c},-1/1}(CP`_{c}) P_{\_G43902} CP`_{c} 

color 200 200 200
drawline h_{M_{c},-1/1}(CP`_{c})
color 0 0 0



% NDG:  line h_{M_{c},-1/1}(CP`_{c}) and circle k_over(I,M_{c}) intersect
% Constructing points C_{fo} and P_{c} which are in intersection of k_over(I,M_{c}) and h_{M_{c},-1/1}(CP`_{c})
intersec2 C_{fo} P_{c} k_over(I,M_{c}) h_{M_{c},-1/1}(CP`_{c}) 
cmark_r C_{fo}
cmark_r P_{c}


% NDG:  points P_{c} and I are not the same
% Constructing a circle k(I,P_{a}) whose center is at point I and which passes through point P_{c}
circle k(I,P_{a}) I P_{c} 

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 midpoint P_{\_G44651} of the segment CI
midpoint P_{\_G44651} C I 
cmark_r P_{\_G44651}

% Constructing a circle C_{\_G44654} whose center is at point P_{\_G44651} and which passes through point C
circle C_{\_G44654} P_{\_G44651} C 

color 200 200 200
drawcircle C_{\_G44654}
color 0 0 0


% Constructing points P_{\_G44657} and P_{\_G44660} which are in intersection of C_{\_G44654} and k(I,P_{a})
intersec2 P_{\_G44657} P_{\_G44660} C_{\_G44654} k(I,P_{a}) 
cmark_r P_{\_G44657}
cmark_r P_{\_G44660}

% Constructing a line a which passes through point C and point P_{\_G44657}
line a C P_{\_G44657} 

color 200 200 200
drawline a
color 0 0 0


% Constructing a line b which passes through point C and point P_{\_G44660}
line b C P_{\_G44660} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  point M_{c} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G45063} of the segment M_{c}I
midpoint P_{\_G45063} M_{c} I 
cmark_r P_{\_G45063}

% Constructing a circle C_{\_G45066} whose center is at point P_{\_G45063} and which passes through point M_{c}
circle C_{\_G45066} P_{\_G45063} M_{c} 

color 200 200 200
drawcircle C_{\_G45066}
color 0 0 0


% Constructing points P_{\_G45069} and P_{\_G45072} which are in intersection of C_{\_G45066} and k(I,P_{a})
intersec2 P_{\_G45069} P_{\_G45072} C_{\_G45066} k(I,P_{a}) 
cmark_r P_{\_G45069}
cmark_r P_{\_G45072}

% Constructing a line x3 which passes through point M_{c} and point P_{\_G45069}
line x3 M_{c} P_{\_G45069} 

color 200 200 200
drawline x3
color 0 0 0


% Constructing a line c which passes through point M_{c} and point P_{\_G45072}
line c M_{c} P_{\_G45072} 

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



% Constructing a point A such that M_{c}A/M_{c}B=-1
towards A M_{c} B -1 
cmark_t A
color 200 200 200
drawsegment B A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a and c are not parallel; point M_{c} is outside the circle k(I,P_{a}); point C is outside the circle k(I,P_{a}); points P_{c} and I are not the same; line h_{M_{c},-1/1}(CP`_{c}) and circle k_over(I,M_{c}) intersect; points I and M_{c} are not the same
% Determination conditions:  lines a and c are not the same; points M_{c} and I are not the same