Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point G 70 58.33
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_t G
cmark_t O
color 0 0 0
fontsize 10


% Constructing a point N such that GN/GO=-0.5
towards N G O -0.5 
cmark_r N
color 200 200 200
drawsegment O N 
color 0 0 0



% Constructing a point H such that GH/GO=-2
towards H G O -2 
cmark_rt H
color 200 200 200
drawsegment O H 
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



% Constructing a point M_{b} such that GM_{b}/GB=-0.5
towards M_{b} G B -0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{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



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

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line h_{b} and circle k(N,M_{a}) intersect% DET:  points E_{b} and H_{b} must be different
% Constructing a point P_{\_G53249} which is a foot of the point N on the line h_{b}
foot P_{\_G53249} N h_{b} 
cmark_r P_{\_G53249}
color 200 200 200
drawline N P_{\_G53249} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point E_{b} in the symmetry to point/line P_{\_G53249}
sim H_{b} P_{\_G53249} E_{b} 
cmark_rt H_{b}


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  points B and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point B
circle k(O,C) O B 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line b and circle k(O,C) intersect
% Constructing points C and A which are in intersection of k(O,C) and b
intersec2 C A k(O,C) b 
cmark_b C
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

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