Construction in GCLC language

dim 120 120

point B 20 40
point G 70 58.33
point I 74.37 61.15

color 220 0 0
fontsize 11

cmark_b B
cmark_t G
cmark_b I
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that BM_{b}/BG=1.5
towards M_{b} B G 1.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0


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

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



% NDG:  points I and M_{b} are not the same
% Constructing midpoint P_{\_G21807} of the segment IM_{b}
midpoint P_{\_G21807} I M_{b} 
cmark_r P_{\_G21807}

% Constructing a circle k_over(I,M_{b}) whose center is at point P_{\_G21807} and which passes through point I
circle k_over(I,M_{b}) P_{\_G21807} 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_{\_G22108} such that M_{b}P_{\_G22108}/M_{b}B=-1
towards P_{\_G22108} M_{b} B -1 
cmark_r P_{\_G22108}
color 200 200 200
drawsegment B P_{\_G22108} 
color 0 0 0

% Constructing a line h_{M_{b},-1/1}(BP`_{b}) which contains the point P_{\_G22108} and is parallel to the line BP`_{b}
parallel h_{M_{b},-1/1}(BP`_{b}) P_{\_G22108} 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_{\_G22857} of the segment BI
midpoint P_{\_G22857} B I 
cmark_r P_{\_G22857}

% Constructing a circle C_{\_G22860} whose center is at point P_{\_G22857} and which passes through point B
circle C_{\_G22860} P_{\_G22857} B 

color 200 200 200
drawcircle C_{\_G22860}
color 0 0 0


% Constructing points P_{\_G22863} and P_{\_G22866} which are in intersection of C_{\_G22860} and k(I,P_{a})
intersec2 P_{\_G22863} P_{\_G22866} C_{\_G22860} k(I,P_{a}) 
cmark_r P_{\_G22863}
cmark_r P_{\_G22866}

% Constructing a line c which passes through point B and point P_{\_G22863}
line c B P_{\_G22863} 

color 200 200 200
drawline c
color 0 0 0


% Constructing a line a which passes through point B and point P_{\_G22866}
line a B P_{\_G22866} 

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_{\_G23269} of the segment M_{b}I
midpoint P_{\_G23269} M_{b} I 
cmark_r P_{\_G23269}

% Constructing a circle C_{\_G23272} whose center is at point P_{\_G23269} and which passes through point M_{b}
circle C_{\_G23272} P_{\_G23269} M_{b} 

color 200 200 200
drawcircle C_{\_G23272}
color 0 0 0


% Constructing points P_{\_G23275} and P_{\_G23278} which are in intersection of C_{\_G23272} and k(I,P_{a})
intersec2 P_{\_G23275} P_{\_G23278} C_{\_G23272} k(I,P_{a}) 
cmark_r P_{\_G23275}
cmark_r P_{\_G23278}

% Constructing a line x2 which passes through point M_{b} and point P_{\_G23275}
line x2 M_{b} P_{\_G23275} 

color 200 200 200
drawline x2
color 0 0 0


% Constructing a line b which passes through point M_{b} and point P_{\_G23278}
line b M_{b} P_{\_G23278} 

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 M_{a} such that GM_{a}/GA=-0.5
towards M_{a} G A -0.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0



% 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



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 I and M_{b} are not the same