Construction in GCLC language
dim 120 120
point A 80 95
point M_{c} 50 67.5
point H 80 72.73
color 220 0 0
fontsize 11
cmark_t A
cmark_lt M_{c}
cmark_rt H
color 0 0 0
fontsize 10
% Constructing a point B such that AB/AM_{c}=2
towards B A M_{c} 2
cmark_b B
color 200 200 200
drawsegment A B
color 0 0 0
% DET: points A and H are not the same
% Constructing a line h_{a} which passes through point A and point H
line h_{a} A H
color 200 200 200
drawline h_{a}
color 0 0 0
% DET: points H and B are not the same
% Constructing a line h_{b} which passes through point H and point B
line h_{b} H B
color 200 200 200
drawline h_{b}
color 0 0 0
% NDG: points A and M_{c} are not the same
% Constructing a circle k(M_{c},A) whose center is at point M_{c} and which passes through point A
circle k(M_{c},A) M_{c} A
color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0
% NDG: line h_{a} and circle k(M_{c},A) intersect% DET: points A and H_{a} must be different
% Constructing a point P_{\_G8423} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G8423} M_{c} h_{a}
cmark_r P_{\_G8423}
color 200 200 200
drawline M_{c} P_{\_G8423}
color 0 0 0
% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G8423}
sim H_{a} P_{\_G8423} A
cmark_b H_{a}
% DET: points H_{a} and B are not the same
% Constructing a line a which passes through point H_{a} and point B
line a H_{a} B
color 200 200 200
drawline a
color 0 0 0
% NDG: line h_{b} and circle k(M_{c},A) intersect% DET: points B and H_{b} must be different
% Constructing a point P_{\_G8661} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G8661} M_{c} h_{b}
cmark_r P_{\_G8661}
color 200 200 200
drawline M_{c} P_{\_G8661}
color 0 0 0
% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G8661}
sim H_{b} P_{\_G8661} B
cmark_rt H_{b}
% DET: points H_{b} and A are not the same
% Constructing a line b which passes through point H_{b} and point A
line b H_{b} A
color 200 200 200
drawline b
color 0 0 0
% NDG: lines a and b are not parallel% DET: lines a and b are not the same
% Constructing a point C which belongs to line a and line b
intersec C a b
cmark_b C
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines a and b are not parallel; line h_{b} and circle k(M_{c},A) intersect; line h_{a} and circle k(M_{c},A) intersect; points A and M_{c} are not the same
% Determination conditions: lines a and b are not the same; points H_{b} and A are not the same; points B and H_{b} must be different; points H_{a} and B are not the same; points A and H_{a} must be different; points H and B are not the same; points A and H are not the same