Construction in GCLC language

dim 120 120

point B 20 40
point M_{b} 95 67.5
point I 74.37 61.15

color 220 0 0
fontsize 11

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

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

color 200 200 200
drawline IM_{b}
color 0 0 0



% NDG:  points I and M_{b} are not the same
% Constructing midpoint P_{\_G26794} of the segment IM_{b}
midpoint P_{\_G26794} I M_{b} 
cmark_r P_{\_G26794}

% Constructing a circle k_over(I,M_{b}) whose center is at point P_{\_G26794} and which passes through point I
circle k_over(I,M_{b}) P_{\_G26794} I 

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




% Constructing a line BP`_{b} which contains the point B and is parallel to the line IM_{b}
parallel BP`_{b} B IM_{b} 

color 200 200 200
drawline BP`_{b}
color 0 0 0




% Constructing a point P_{\_G27095} such that M_{b}P_{\_G27095}/M_{b}B=-1
towards P_{\_G27095} M_{b} B -1 
cmark_r P_{\_G27095}
color 200 200 200
drawsegment B P_{\_G27095} 
color 0 0 0

% Constructing a line h_{M_{b},-1/1}(BP`_{b}) which contains the point P_{\_G27095} and is parallel to the line BP`_{b}
parallel h_{M_{b},-1/1}(BP`_{b}) P_{\_G27095} BP`_{b} 

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



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


% NDG:  points P_{b} 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_{b}
circle k(I,P_{a}) I P_{b} 

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 midpoint P_{\_G27844} of the segment BI
midpoint P_{\_G27844} B I 
cmark_r P_{\_G27844}

% Constructing a circle C_{\_G27847} whose center is at point P_{\_G27844} and which passes through point B
circle C_{\_G27847} P_{\_G27844} B 

color 200 200 200
drawcircle C_{\_G27847}
color 0 0 0


% Constructing points P_{\_G27850} and P_{\_G27853} which are in intersection of C_{\_G27847} and k(I,P_{a})
intersec2 P_{\_G27850} P_{\_G27853} C_{\_G27847} k(I,P_{a}) 
cmark_r P_{\_G27850}
cmark_r P_{\_G27853}

% Constructing a line c which passes through point B and point P_{\_G27850}
line c B P_{\_G27850} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line a which passes through point B and point P_{\_G27853}
line a B P_{\_G27853} 

color 200 200 200
drawline a
color 0 0 0



% NDG:  point M_{b} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G28256} of the segment M_{b}I
midpoint P_{\_G28256} M_{b} I 
cmark_r P_{\_G28256}

% Constructing a circle C_{\_G28259} whose center is at point P_{\_G28256} and which passes through point M_{b}
circle C_{\_G28259} P_{\_G28256} M_{b} 

color 200 200 200
drawcircle C_{\_G28259}
color 0 0 0


% Constructing points P_{\_G28262} and P_{\_G28265} which are in intersection of C_{\_G28259} and k(I,P_{a})
intersec2 P_{\_G28262} P_{\_G28265} C_{\_G28259} k(I,P_{a}) 
cmark_r P_{\_G28262}
cmark_r P_{\_G28265}

% Constructing a line x2 which passes through point M_{b} and point P_{\_G28262}
line x2 M_{b} P_{\_G28262} 

color 200 200 200
drawline x2
color 0 0 0


% Constructing a line b which passes through point M_{b} and point P_{\_G28265}
line b M_{b} P_{\_G28265} 

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



% Constructing a point C such that M_{b}C/M_{b}A=-1
towards C M_{b} A -1 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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