Construction in GCLC language
dim 120 120
point M_{c} 50 67.5
point G 70 58.33
point I 74.37 61.15
color 220 0 0
fontsize 11
cmark_lt M_{c}
cmark_t G
cmark_b I
color 0 0 0
fontsize 10
% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3
cmark_b C
color 200 200 200
drawsegment M_{c} C
color 0 0 0
% 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
% DET: points I and C are not the same
% Constructing a line s_{c} which passes through point I and point C
line s_{c} I C
color 200 200 200
drawline s_{c}
color 0 0 0
% NDG: points I and M_{c} are not the same
% Constructing midpoint P_{\_G46570} of the segment IM_{c}
midpoint P_{\_G46570} I M_{c}
cmark_r P_{\_G46570}
% Constructing a circle k_over(I,M_{c}) whose center is at point P_{\_G46570} and which passes through point I
circle k_over(I,M_{c}) P_{\_G46570} 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_{\_G46871} such that M_{c}P_{\_G46871}/M_{c}C=-1
towards P_{\_G46871} M_{c} C -1
cmark_r P_{\_G46871}
color 200 200 200
drawsegment C P_{\_G46871}
color 0 0 0
% Constructing a line h_{M_{c},-1/1}(CP`_{c}) which contains the point P_{\_G46871} and is parallel to the line CP`_{c}
parallel h_{M_{c},-1/1}(CP`_{c}) P_{\_G46871} 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 M_{c} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G47620} of the segment M_{c}I
midpoint P_{\_G47620} M_{c} I
cmark_r P_{\_G47620}
% Constructing a circle C_{\_G47623} whose center is at point P_{\_G47620} and which passes through point M_{c}
circle C_{\_G47623} P_{\_G47620} M_{c}
color 200 200 200
drawcircle C_{\_G47623}
color 0 0 0
% Constructing points P_{\_G47626} and P_{\_G47629} which are in intersection of C_{\_G47623} and k(I,P_{a})
intersec2 P_{\_G47626} P_{\_G47629} C_{\_G47623} k(I,P_{a})
cmark_r P_{\_G47626}
cmark_r P_{\_G47629}
% Constructing a line x3 which passes through point M_{c} and point P_{\_G47626}
line x3 M_{c} P_{\_G47626}
color 200 200 200
drawline x3
color 0 0 0
% Constructing a line c which passes through point M_{c} and point P_{\_G47629}
line c M_{c} P_{\_G47629}
color 200 200 200
drawline c
color 0 0 0
% Constructing a line m_{c} which is perpendicular to line c and which passes through point M_{c}
perp m_{c} M_{c} c
color 200 200 200
drawline m_{c}
color 0 0 0
% NDG: lines m_{c} and s_{c} are not parallel% DET: lines m_{c} and s_{c} are not the same
% Constructing a point N_{c} which belongs to line m_{c} and line s_{c}
intersec N_{c} m_{c} s_{c}
cmark_b N_{c}
% NDG: points I and N_{c} are not the same
% Constructing a circle k(N_{c},B) whose center is at point N_{c} and which passes through point I
circle k(N_{c},B) N_{c} I
color 200 200 200
drawcircle k(N_{c},B)
color 0 0 0
% NDG: line c and circle k(N_{c},B) intersect
% Constructing points B and A which are in intersection of k(N_{c},B) and c
intersec2 B A k(N_{c},B) c
cmark_b B
cmark_t A
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: line c and circle k(N_{c},B) intersect; points I and N_{c} are not the same; lines m_{c} and s_{c} are not parallel; point M_{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 m_{c} and s_{c} are not the same; points I and C are not the same; points M_{c} and I are not the same