Construction in GCLC language
dim 120 120
point M_{a} 65 40
point H_{b} 89.36 77.83
point H 80 72.73
color 220 0 0
fontsize 11
cmark_b M_{a}
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_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point H_{b}
circle k(M_{a},B) M_{a} H_{b}
color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0
% NDG: line h_{b} and circle k(M_{a},B) intersect% DET: points H_{b} and B must be different
% Constructing a point P_{\_G61471} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G61471} M_{a} h_{b}
cmark_r P_{\_G61471}
color 200 200 200
drawline M_{a} P_{\_G61471}
color 0 0 0
% Constructing a point B which is an image of the point H_{b} in the symmetry to point/line P_{\_G61471}
sim B P_{\_G61471} H_{b}
cmark_b B
% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2
cmark_b C
color 200 200 200
drawsegment B C
color 0 0 0
% DET: points H_{b} and C are not the same
% Constructing a line b which passes through point H_{b} and point C
line b H_{b} C
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: line h_{c} and circle k(M_{a},B) intersect% DET: points C and H_{c} must be different
% Constructing a point P_{\_G61834} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G61834} M_{a} h_{c}
cmark_r P_{\_G61834}
color 200 200 200
drawline M_{a} P_{\_G61834}
color 0 0 0
% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G61834}
sim H_{c} P_{\_G61834} C
cmark_lt H_{c}
% DET: points B and H_{c} are not the same
% Constructing a line c which passes through point B and point H_{c}
line c B H_{c}
color 200 200 200
drawline c
color 0 0 0
% NDG: lines b and c are not parallel% DET: lines b and c are not the same
% Constructing a point A which belongs to line b and line c
intersec A b c
cmark_t A
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines b and c are not parallel; line h_{c} and circle k(M_{a},B) intersect; line h_{b} and circle k(M_{a},B) intersect; points H_{b} and M_{a} are not the same
% Determination conditions: lines b and c are not the same; points B and H_{c} are not the same; points C and H_{c} must be different; points H and C are not the same; points H_{b} and C are not the same; points H_{b} and B must be different; points H_{b} and H are not the same