Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point G 70 58.33
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{a}
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 A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0



% Constructing a point M_{a} such that GM_{a}/GA=-0.5
towards M_{a} G A -0.5 
cmark_b M_{a}
color 200 200 200
drawsegment A M_{a} 
color 0 0 0


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

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



% NDG:  points E_{a} 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_{a}
circle k(N,M_{a}) N E_{a} 

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



% NDG:  line h_{a} and circle k(N,M_{a}) intersect% DET:  points E_{a} and H_{a} must be different
% Constructing a point P_{\_G63692} which is a foot of the point N on the line h_{a}
foot P_{\_G63692} N h_{a} 
cmark_r P_{\_G63692}
color 200 200 200
drawline N P_{\_G63692} 
color 0 0 0

% Constructing a point H_{a} which is an image of the point E_{a} in the symmetry to point/line P_{\_G63692}
sim H_{a} P_{\_G63692} E_{a} 
cmark_b H_{a}


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

color 200 200 200
drawline a
color 0 0 0



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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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