Construction in GCLC language
dim 120 120
point M_{c} 50 67.5
point H_{b} 89.36 77.83
point H 80 72.73
color 220 0 0
fontsize 11
cmark_lt M_{c}
cmark_rt H_{b}
cmark_rt H
color 0 0 0
fontsize 10
% 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: points H_{b} 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 H_{b}
circle k(M_{c},A) M_{c} H_{b}
color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0
% NDG: line h_{b} and circle k(M_{c},A) intersect% DET: points H_{b} and B must be different
% Constructing a point P_{\_G64552} which is a foot of the point M_{c} on the line h_{b}
foot P_{\_G64552} M_{c} h_{b}
cmark_r P_{\_G64552}
color 200 200 200
drawline M_{c} P_{\_G64552}
color 0 0 0
% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line P_{\_G64552}
sim B P_{\_G64552} H_{b}
cmark_b B
% Constructing a point A such that BA/BM_{c}=2
towards A B M_{c} 2
cmark_t A
color 200 200 200
drawsegment B A
color 0 0 0
% 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
% DET: points H and A are not the same
% Constructing a line h_{a} which passes through point H and point A
line h_{a} H A
color 200 200 200
drawline h_{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_{\_G64915} which is a foot of the point M_{c} on the line h_{a}
foot P_{\_G64915} M_{c} h_{a}
cmark_r P_{\_G64915}
color 200 200 200
drawline M_{c} P_{\_G64915}
color 0 0 0
% Constructing a point H_{a} which is an image of the point A in the symmetry to point/line P_{\_G64915}
sim H_{a} P_{\_G64915} A
cmark_b H_{a}
% DET: points B and H_{a} are not the same
% Constructing a line a which passes through point B and point H_{a}
line a B H_{a}
color 200 200 200
drawline a
color 0 0 0
% NDG: lines b and a are not parallel% DET: lines b and a are not the same
% Constructing a point C which belongs to line b and line a
intersec C b a
cmark_b C
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines b and a are not parallel; line h_{a} and circle k(M_{c},A) intersect; line h_{b} and circle k(M_{c},A) intersect; points H_{b} and M_{c} are not the same
% Determination conditions: lines b and a are not the same; points B and H_{a} are not the same; points A and H_{a} must be different; points H and A are not the same; points H_{b} and A are not the same; points H_{b} and B must be different; points H_{b} and H are not the same