Construction in GCLC language
dim 120 120
point M_{a} 65 40
point G 70 58.33
point I 74.37 61.15
color 220 0 0
fontsize 11
cmark_b M_{a}
cmark_t G
cmark_b I
color 0 0 0
fontsize 10
% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3
cmark_t A
color 200 200 200
drawsegment M_{a} A
color 0 0 0
% DET: points M_{a} and I are not the same
% Constructing a line IM_{a} which passes through point M_{a} and point I
line IM_{a} M_{a} I
color 200 200 200
drawline IM_{a}
color 0 0 0
% DET: points I and A are not the same
% Constructing a line s_{a} which passes through point I and point A
line s_{a} I A
color 200 200 200
drawline s_{a}
color 0 0 0
% NDG: points I and M_{a} are not the same
% Constructing midpoint P_{\_G40403} of the segment IM_{a}
midpoint P_{\_G40403} I M_{a}
cmark_r P_{\_G40403}
% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G40403} and which passes through point I
circle k_over(I,M_{a}) P_{\_G40403} I
color 200 200 200
drawcircle k_over(I,M_{a})
color 0 0 0
% Constructing a line AP`_{a} which contains the point A and is parallel to the line IM_{a}
parallel AP`_{a} A IM_{a}
color 200 200 200
drawline AP`_{a}
color 0 0 0
% Constructing a point P_{\_G40704} such that M_{a}P_{\_G40704}/M_{a}A=-1
towards P_{\_G40704} M_{a} A -1
cmark_r P_{\_G40704}
color 200 200 200
drawsegment A P_{\_G40704}
color 0 0 0
% Constructing a line h_{M_{a},-1/1}(AP`_{a}) which contains the point P_{\_G40704} and is parallel to the line AP`_{a}
parallel h_{M_{a},-1/1}(AP`_{a}) P_{\_G40704} AP`_{a}
color 200 200 200
drawline h_{M_{a},-1/1}(AP`_{a})
color 0 0 0
% NDG: line h_{M_{a},-1/1}(AP`_{a}) and circle k_over(I,M_{a}) intersect
% Constructing points A_{fo} and P_{a} which are in intersection of k_over(I,M_{a}) and h_{M_{a},-1/1}(AP`_{a})
intersec2 A_{fo} P_{a} k_over(I,M_{a}) h_{M_{a},-1/1}(AP`_{a})
cmark_r A_{fo}
cmark_r P_{a}
% NDG: points P_{a} 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_{a}
circle k(I,P_{a}) I P_{a}
color 200 200 200
drawcircle k(I,P_{a})
color 0 0 0
% NDG: point M_{a} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G41453} of the segment M_{a}I
midpoint P_{\_G41453} M_{a} I
cmark_r P_{\_G41453}
% Constructing a circle C_{\_G41456} whose center is at point P_{\_G41453} and which passes through point M_{a}
circle C_{\_G41456} P_{\_G41453} M_{a}
color 200 200 200
drawcircle C_{\_G41456}
color 0 0 0
% Constructing points P_{\_G41459} and P_{\_G41462} which are in intersection of C_{\_G41456} and k(I,P_{a})
intersec2 P_{\_G41459} P_{\_G41462} C_{\_G41456} k(I,P_{a})
cmark_r P_{\_G41459}
cmark_r P_{\_G41462}
% Constructing a line x1 which passes through point M_{a} and point P_{\_G41459}
line x1 M_{a} P_{\_G41459}
color 200 200 200
drawline x1
color 0 0 0
% Constructing a line a which passes through point M_{a} and point P_{\_G41462}
line a M_{a} P_{\_G41462}
color 200 200 200
drawline a
color 0 0 0
% Constructing a line m_{a} which is perpendicular to line a and which passes through point M_{a}
perp m_{a} M_{a} a
color 200 200 200
drawline m_{a}
color 0 0 0
% NDG: lines m_{a} and s_{a} are not parallel% DET: lines m_{a} and s_{a} are not the same
% Constructing a point N_{a} which belongs to line m_{a} and line s_{a}
intersec N_{a} m_{a} s_{a}
cmark_b N_{a}
% NDG: points I and N_{a} are not the same
% Constructing a circle k(N_{a},C) whose center is at point N_{a} and which passes through point I
circle k(N_{a},C) N_{a} I
color 200 200 200
drawcircle k(N_{a},C)
color 0 0 0
% NDG: line a and circle k(N_{a},C) intersect
% Constructing points C and B which are in intersection of k(N_{a},C) and a
intersec2 C B k(N_{a},C) a
cmark_b C
cmark_b B
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: line a and circle k(N_{a},C) intersect; points I and N_{a} are not the same; lines m_{a} and s_{a} are not parallel; point M_{a} is outside the circle k(I,P_{a}); points P_{a} and I are not the same; line h_{M_{a},-1/1}(AP`_{a}) and circle k_over(I,M_{a}) intersect; points I and M_{a} are not the same
% Determination conditions: lines m_{a} and s_{a} are not the same; points I and A are not the same; points M_{a} and I are not the same