Construction in GCLC language
dim 120 120
point A 80 95
point E_{a} 80 83.86
point M_{b} 95 67.5
color 220 0 0
fontsize 11
cmark_t A
cmark_r E_{a}
cmark_rt M_{b}
color 0 0 0
fontsize 10
% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2
cmark_rt H
color 200 200 200
drawsegment A H
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
% DET: points A and M_{b} are not the same
% Constructing a line b which passes through point A and point M_{b}
line b A M_{b}
color 200 200 200
drawline b
color 0 0 0
% DET: points H and C are not the same
% Constructing a line h_{c} which passes through point H and point C
line h_{c} H C
color 200 200 200
drawline h_{c}
color 0 0 0
% NDG: points A and E_{a} are not the same
% Constructing a circle k(E_{a},A) whose center is at point E_{a} and which passes through point A
circle k(E_{a},A) E_{a} A
color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0
% NDG: line b and circle k(E_{a},A) intersect% DET: points A and H_{b} must be different
% Constructing a point P_{\_G12262} which is a foot of the point E_{a} on the line b
foot P_{\_G12262} E_{a} b
cmark_r P_{\_G12262}
color 200 200 200
drawline E_{a} P_{\_G12262}
color 0 0 0
% Constructing a point H_{b} which is an image of the point A in the symmetry to point/line P_{\_G12262}
sim H_{b} P_{\_G12262} A
cmark_rt H_{b}
% DET: points H_{b} and H are not the same
% Constructing a line h_{b} which passes through point H_{b} and point H
line h_{b} H_{b} H
color 200 200 200
drawline h_{b}
color 0 0 0
% NDG: line h_{c} and circle k(E_{a},A) intersect% DET: points H and H_{c} must be different
% Constructing a point P_{\_G12500} which is a foot of the point E_{a} on the line h_{c}
foot P_{\_G12500} E_{a} h_{c}
cmark_r P_{\_G12500}
color 200 200 200
drawline E_{a} P_{\_G12500}
color 0 0 0
% Constructing a point H_{c} which is an image of the point H in the symmetry to point/line P_{\_G12500}
sim H_{c} P_{\_G12500} H
cmark_lt H_{c}
% DET: points H_{c} and A are not the same
% Constructing a line c which passes through point H_{c} and point A
line c H_{c} A
color 200 200 200
drawline c
color 0 0 0
% NDG: lines h_{b} and c are not parallel% DET: lines h_{b} and c are not the same
% Constructing a point B which belongs to line h_{b} and line c
intersec B h_{b} c
cmark_b B
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines h_{b} and c are not parallel; line h_{c} and circle k(E_{a},A) intersect; line b and circle k(E_{a},A) intersect; points A and E_{a} are not the same
% Determination conditions: lines h_{b} and c are not the same; points H_{c} and A are not the same; points H and H_{c} must be different; points H_{b} and H are not the same; points A and H_{b} must be different; points H and C are not the same; points A and M_{b} are not the same