Construction in GCLC language
dim 120 120
point E_{b} 50 56.36
point E_{c} 95 56.36
point H_{c} 68.91 84.83
color 220 0 0
fontsize 11
cmark_r E_{b}
cmark_r E_{c}
cmark_lt H_{c}
color 0 0 0
fontsize 10
% DET: points E_{c} and H_{c} are not the same
% Constructing a line h_{c} which passes through point E_{c} and point H_{c}
line h_{c} E_{c} H_{c}
color 200 200 200
drawline h_{c}
color 0 0 0
% NDG: points H_{c} and E_{b} are not the same
% Constructing a circle k(E_{b},B) whose center is at point E_{b} and which passes through point H_{c}
circle k(E_{b},B) E_{b} H_{c}
color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0
% NDG: line h_{c} and circle k(E_{b},B) intersect% DET: points H_{c} and H must be different
% Constructing a point P_{\_G42840} which is a foot of the point E_{b} on the line h_{c}
foot P_{\_G42840} E_{b} h_{c}
cmark_r P_{\_G42840}
color 200 200 200
drawline E_{b} P_{\_G42840}
color 0 0 0
% Constructing a point H which is an image of the point H_{c} in the symmetry to point/line P_{\_G42840}
sim H P_{\_G42840} H_{c}
cmark_rt H
% Constructing a point B such that HB/HE_{b}=2
towards B H E_{b} 2
cmark_b B
color 200 200 200
drawsegment H B
color 0 0 0
% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1
cmark_b C
color 200 200 200
drawsegment H C
color 0 0 0
% 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
% DET: points B and C are not the same
% Constructing a line a which passes through point B and point C
line a B C
color 200 200 200
drawline a
color 0 0 0
% NDG: line a and circle k(E_{b},B) intersect% DET: points B and H_{a} must be different
% Constructing a point P_{\_G43277} which is a foot of the point E_{b} on the line a
foot P_{\_G43277} E_{b} a
cmark_r P_{\_G43277}
color 200 200 200
drawline E_{b} P_{\_G43277}
color 0 0 0
% Constructing a point H_{a} which is an image of the point B in the symmetry to point/line P_{\_G43277}
sim H_{a} P_{\_G43277} B
cmark_b H_{a}
% DET: points H and H_{a} are not the same
% Constructing a line h_{a} which passes through point H and point H_{a}
line h_{a} H H_{a}
color 200 200 200
drawline h_{a}
color 0 0 0
% NDG: lines c and h_{a} are not parallel% DET: lines c and h_{a} are not the same
% Constructing a point A which belongs to line c and line h_{a}
intersec A c h_{a}
cmark_t A
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: lines c and h_{a} are not parallel; line a and circle k(E_{b},B) intersect; line h_{c} and circle k(E_{b},B) intersect; points H_{c} and E_{b} are not the same
% Determination conditions: lines c and h_{a} are not the same; points H and H_{a} are not the same; points B and H_{a} must be different; points B and C are not the same; points H_{c} and B are not the same; points H_{c} and H must be different; points E_{c} and H_{c} are not the same