Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point E_{b} 50 56.36
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_r E_{b}
cmark_lt H_{c}
color 0 0 0
fontsize 10

% NDG:  points H_{c} and E_{a} are not the same
% Constructing a circle k(E_{a},A) whose center is at point E_{a} and which passes through point H_{c}
circle k(E_{a},A) E_{a} H_{c} 

color 200 200 200
drawcircle k(E_{a},A)
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:  circles k(E_{a},A) and k(E_{b},B) intersect% DET:  circles k(E_{a},A) and k(E_{b},B) are not the same; points H_{c} and H must be different
% Constructing a line L_{\_G19733} which passes through point E_{a} and point E_{b}
line L_{\_G19733} E_{a} E_{b} 

color 200 200 200
drawline L_{\_G19733}
color 0 0 0


% Constructing a point H which is an image of the point H_{c} in the symmetry to point/line L_{\_G19733}
sim H L_{\_G19733} H_{c} 
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 E_{b} and H are not the same
% Constructing a line h_{b} which passes through point E_{b} and point H
line h_{b} E_{b} H 

color 200 200 200
drawline h_{b}
color 0 0 0



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

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



% NDG:  line h_{b} and circle k(E_{a},A) intersect% DET:  points H and H_{b} must be different
% Constructing a point P_{\_G20150} which is a foot of the point E_{a} on the line h_{b}
foot P_{\_G20150} E_{a} h_{b} 
cmark_r P_{\_G20150}
color 200 200 200
drawline E_{a} P_{\_G20150} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point H in the symmetry to point/line P_{\_G20150}
sim H_{b} P_{\_G20150} H 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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