Construction in GCLC language
dim 120 120
point C 110 40
point G 70 58.33
point I 74.37 61.15
color 220 0 0
fontsize 11
cmark_b C
cmark_t G
cmark_b I
color 0 0 0
fontsize 10
% Constructing a point M_{c} such that CM_{c}/CG=1.5
towards M_{c} C G 1.5
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c}
color 0 0 0
% DET: points I and M_{c} are not the same
% Constructing a line IM_{c} which passes through point I and point M_{c}
line IM_{c} I M_{c}
color 200 200 200
drawline IM_{c}
color 0 0 0
% NDG: points I and M_{c} are not the same
% Constructing midpoint P_{\_G37415} of the segment IM_{c}
midpoint P_{\_G37415} I M_{c}
cmark_r P_{\_G37415}
% Constructing a circle k_over(I,M_{c}) whose center is at point P_{\_G37415} and which passes through point I
circle k_over(I,M_{c}) P_{\_G37415} 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_{\_G37716} such that M_{c}P_{\_G37716}/M_{c}C=-1
towards P_{\_G37716} M_{c} C -1
cmark_r P_{\_G37716}
color 200 200 200
drawsegment C P_{\_G37716}
color 0 0 0
% Constructing a line h_{M_{c},-1/1}(CP`_{c}) which contains the point P_{\_G37716} and is parallel to the line CP`_{c}
parallel h_{M_{c},-1/1}(CP`_{c}) P_{\_G37716} 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_{\_G38465} of the segment CI
midpoint P_{\_G38465} C I
cmark_r P_{\_G38465}
% Constructing a circle C_{\_G38468} whose center is at point P_{\_G38465} and which passes through point C
circle C_{\_G38468} P_{\_G38465} C
color 200 200 200
drawcircle C_{\_G38468}
color 0 0 0
% Constructing points P_{\_G38471} and P_{\_G38474} which are in intersection of C_{\_G38468} and k(I,P_{a})
intersec2 P_{\_G38471} P_{\_G38474} C_{\_G38468} k(I,P_{a})
cmark_r P_{\_G38471}
cmark_r P_{\_G38474}
% Constructing a line a which passes through point C and point P_{\_G38471}
line a C P_{\_G38471}
color 200 200 200
drawline a
color 0 0 0
% Constructing a line b which passes through point C and point P_{\_G38474}
line b C P_{\_G38474}
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_{\_G38877} of the segment M_{c}I
midpoint P_{\_G38877} M_{c} I
cmark_r P_{\_G38877}
% Constructing a circle C_{\_G38880} whose center is at point P_{\_G38877} and which passes through point M_{c}
circle C_{\_G38880} P_{\_G38877} M_{c}
color 200 200 200
drawcircle C_{\_G38880}
color 0 0 0
% Constructing points P_{\_G38883} and P_{\_G38886} which are in intersection of C_{\_G38880} and k(I,P_{a})
intersec2 P_{\_G38883} P_{\_G38886} C_{\_G38880} k(I,P_{a})
cmark_r P_{\_G38883}
cmark_r P_{\_G38886}
% Constructing a line x3 which passes through point M_{c} and point P_{\_G38883}
line x3 M_{c} P_{\_G38883}
color 200 200 200
drawline x3
color 0 0 0
% Constructing a line c which passes through point M_{c} and point P_{\_G38886}
line c M_{c} P_{\_G38886}
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 M_{b} such that GM_{b}/GB=-0.5
towards M_{b} G B -0.5
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b}
color 0 0 0
% 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
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 I and M_{c} are not the same