Construction in GCLC language
dim 120 120
point A 80 95
point G 70 58.33
point I 74.37 61.15
color 220 0 0
fontsize 11
cmark_t A
cmark_t G
cmark_b I
color 0 0 0
fontsize 10
% Constructing a point M_{a} such that AM_{a}/AG=1.5
towards M_{a} A G 1.5
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a}
color 0 0 0
% DET: points I and M_{a} are not the same
% Constructing a line IM_{a} which passes through point I and point M_{a}
line IM_{a} I M_{a}
color 200 200 200
drawline IM_{a}
color 0 0 0
% NDG: points I and M_{a} are not the same
% Constructing midpoint P_{\_G14724} of the segment IM_{a}
midpoint P_{\_G14724} I M_{a}
cmark_r P_{\_G14724}
% Constructing a circle k_over(I,M_{a}) whose center is at point P_{\_G14724} and which passes through point I
circle k_over(I,M_{a}) P_{\_G14724} 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_{\_G15025} such that M_{a}P_{\_G15025}/M_{a}A=-1
towards P_{\_G15025} M_{a} A -1
cmark_r P_{\_G15025}
color 200 200 200
drawsegment A P_{\_G15025}
color 0 0 0
% Constructing a line h_{M_{a},-1/1}(AP`_{a}) which contains the point P_{\_G15025} and is parallel to the line AP`_{a}
parallel h_{M_{a},-1/1}(AP`_{a}) P_{\_G15025} 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 A is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G15774} of the segment AI
midpoint P_{\_G8814} A I
cmark_r P_{\_G8814}
% Constructing a circle C_{\_G15777} whose center is at point P_{\_G15774} and which passes through point A
circle C_{\_G8817} P_{\_G8814} A
color 200 200 200
drawcircle C_{\_G8817}
color 0 0 0
% Constructing points P_{\_G15780} and P_{\_G15783} which are in intersection of C_{\_G15777} and k(I,P_{a})
intersec2 P_{\_G8820} P_{\_G8823} C_{\_G8817} k(I,P_{a})
cmark_r P_{\_G8820}
cmark_r P_{\_G8823}
% Constructing a line c which passes through point A and point P_{\_G8820}
line c A P_{\_G8820}
color 200 200 200
drawline c
color 0 0 0
% Constructing a line b which passes through point A and point P_{\_G8823}
line b A P_{\_G8823}
color 200 200 200
drawline b
color 0 0 0
% NDG: point M_{a} is outside the circle k(I,P_{a})
% Constructing midpoint P_{\_G9148} of the segment M_{a}I
midpoint P_{\_G9148} M_{a} I
cmark_r P_{\_G9148}
% Constructing a circle C_{\_G9151} whose center is at point P_{\_G9148} and which passes through point M_{a}
circle C_{\_G9151} P_{\_G9148} M_{a}
color 200 200 200
drawcircle C_{\_G9151}
color 0 0 0
% Constructing points P_{\_G9154} and P_{\_G9157} which are in intersection of C_{\_G9151} and k(I,P_{a})
intersec2 P_{\_G9154} P_{\_G9157} C_{\_G9151} k(I,P_{a})
cmark_r P_{\_G9154}
cmark_r P_{\_G9157}
% Constructing a line x1 which passes through point M_{a} and point P_{\_G9154}
line x1 M_{a} P_{\_G9154}
color 200 200 200
drawline x1
color 0 0 0
% Constructing a line a which passes through point M_{a} and point P_{\_G9157}
line a M_{a} P_{\_G9157}
color 200 200 200
drawline a
color 0 0 0
% NDG: lines c and a are not parallel% DET: lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a
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 C such that AC/AM_{b}=2
towards C A M_{b} 2
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 a are not parallel; point M_{a} is outside the circle k(I,P_{a}); point 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 c and a are not the same; points I and M_{a} are not the same