Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point H 80 72.73
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{b}
cmark_rt H
cmark_t O
color 0 0 0
fontsize 10


% 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 N such that HN/HO=0.5
towards N H O 0.5 
cmark_r N
color 200 200 200
drawsegment H O 
color 0 0 0



% Constructing a line L_{\_G59419} which passes through point H and point O
line L_{\_G59419} H O 

color 200 200 200
drawline L_{\_G59419}
color 0 0 0


% Constructing a point P_{\_G59520} with coordinates (0,0)
point P_{\_G59520} 0 0 
cmark_r P_{\_G59520}

% Constructing a point P_{\_G59444} such that HP_{\_G59444}/HP_{\_G59520}=2
towards P_{\_G59444} H P_{\_G59520} 2 
cmark_r P_{\_G59444}
color 200 200 200
drawsegment H P_{\_G59444} 
color 0 0 0

% Constructing a point P_{\_G59489} such that HP_{\_G59489}/HP_{\_G59520}=3
towards P_{\_G59489} H P_{\_G59520} 3 
cmark_r P_{\_G59489}
color 200 200 200
drawsegment H P_{\_G59489} 
color 0 0 0

% Constructing a line L_{\_G59450} which passes through point O and point P_{\_G59489}
line L_{\_G59450} O P_{\_G59489} 

color 200 200 200
drawline L_{\_G59450}
color 0 0 0


% Constructing a line L_{\_G59413} which contains the point P_{\_G59444} and is parallel to the line L_{\_G59450}
parallel L_{\_G59413} P_{\_G59444} L_{\_G59450} 

color 200 200 200
drawline L_{\_G59413}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G59413} and line L_{\_G59419}
intersec G L_{\_G59413} L_{\_G59419} 
cmark_t G



% Constructing a point M_{b} such that BM_{b}/BG=1.5
towards M_{b} B G 1.5 
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_{\_G60356} which is a foot of the point N on the line h_{b}
foot P_{\_G60356} N h_{b} 
cmark_r P_{\_G60356}
color 200 200 200
drawline N P_{\_G60356} 
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_{\_G60356}
sim H_{b} P_{\_G60356} 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