Construction in GCLC language
dim 120 120
point C 110 40
point M_{a} 65 40
point H 80 72.73
color 220 0 0
fontsize 11
cmark_b C
cmark_b M_{a}
cmark_rt H
color 0 0 0
fontsize 10
% Constructing a point B such that CB/CM_{a}=2
towards B C M_{a} 2
cmark_b B
color 200 200 200
drawsegment C B
color 0 0 0
% DET: points C and H are not the same
% Constructing a line h_{c} which passes through point C and point H
line h_{c} C H
color 200 200 200
drawline h_{c}
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 C 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 C
circle k(M_{a},B) M_{a} C
color 200 200 200
drawcircle k(M_{a},B)
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_{\_G27570} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G27570} M_{a} h_{c}
cmark_r P_{\_G27570}
color 200 200 200
drawline M_{a} P_{\_G27570}
color 0 0 0
% Constructing a point H_{c} which is an image of the point C in the symmetry to point/line P_{\_G27570}
sim H_{c} P_{\_G27570} C
cmark_lt H_{c}
% DET: points H_{c} and B are not the same
% Constructing a line c which passes through point H_{c} and point B
line c H_{c} B
color 200 200 200
drawline c
color 0 0 0
% NDG: line h_{b} and circle k(M_{a},B) intersect% DET: points B and H_{b} must be different
% Constructing a point P_{\_G27808} which is a foot of the point M_{a} on the line h_{b}
foot P_{\_G27808} M_{a} h_{b}
cmark_r P_{\_G27808}
color 200 200 200
drawline M_{a} P_{\_G27808}
color 0 0 0
% Constructing a point H_{b} which is an image of the point B in the symmetry to point/line P_{\_G27808}
sim H_{b} P_{\_G27808} B
cmark_rt H_{b}
% 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
% NDG: lines c and b are not parallel% DET: lines c and b are not the same
% Constructing a point A which belongs to line c and line b
intersec A c b
cmark_t A
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines c and b are not parallel; line h_{b} and circle k(M_{a},B) intersect; line h_{c} and circle k(M_{a},B) intersect; points C and M_{a} are not the same
% Determination conditions: lines c and b are not the same; points H_{b} and C are not the same; points B and H_{b} must be different; points H_{c} and B are not the same; points C and H_{c} must be different; points H and B are not the same; points C and H are not the same