Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{b} 50 56.36
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_r E_{b}
cmark_b H_{a}
color 0 0 0
fontsize 10

% DET:  points E_{a} and H_{a} are not the same
% Constructing a line h_{a} which passes through point E_{a} and point H_{a}
line h_{a} E_{a} H_{a} 

color 200 200 200
drawline h_{a}
color 0 0 0



% NDG:  points H_{a} 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_{a}
circle k(E_{b},B) E_{b} H_{a} 

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  line h_{a} and circle k(E_{b},B) intersect% DET:  points H_{a} and H must be different
% Constructing a point P_{\_G21218} which is a foot of the point E_{b} on the line h_{a}
foot P_{\_G21218} E_{b} h_{a} 
cmark_r P_{\_G21218}
color 200 200 200
drawline E_{b} P_{\_G21218} 
color 0 0 0

% Constructing a point H which is an image of the point H_{a} in the symmetry to point/line P_{\_G21218}
sim H P_{\_G21218} H_{a} 
cmark_rt H



% Constructing a point A such that HA/HE_{a}=2
towards A H E_{a} 2 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0


% 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



% DET:  points A and B are not the same
% Constructing a line c which passes through point A and point B
line c A B 

color 200 200 200
drawline c
color 0 0 0



% NDG:  line c and circle k(E_{b},B) intersect% DET:  points B and H_{c} must be different
% Constructing a point P_{\_G21655} which is a foot of the point E_{b} on the line c
foot P_{\_G21655} E_{b} c 
cmark_r P_{\_G21655}
color 200 200 200
drawline E_{b} P_{\_G21655} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point B in the symmetry to point/line P_{\_G21655}
sim H_{c} P_{\_G21655} B 
cmark_lt H_{c}


% DET:  points H and H_{c} are not the same
% Constructing a line h_{c} which passes through point H and point H_{c}
line h_{c} H H_{c} 

color 200 200 200
drawline h_{c}
color 0 0 0



% NDG:  lines a and h_{c} are not parallel% DET:  lines a and h_{c} are not the same
% Constructing a point C which belongs to line a and line h_{c}
intersec C a h_{c} 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a and h_{c} are not parallel; line c and circle k(E_{b},B) intersect; line h_{a} and circle k(E_{b},B) intersect; points H_{a} and E_{b} are not the same
% Determination conditions:  lines a and h_{c} are not the same; points H and H_{c} are not the same; points B and H_{c} must be different; points A and B are not the same; points H_{a} and B are not the same; points H_{a} and H must be different; points E_{a} and H_{a} are not the same