Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_rt H_{b}
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G47031} which passes through point N and point O
line L_{\_G47031} N O 

color 200 200 200
drawline L_{\_G47031}
color 0 0 0


% Constructing a point P_{\_G47132} with coordinates (0,0)
point P_{\_G47132} 0 0 
cmark_r P_{\_G47132}

% Constructing a point P_{\_G47056} such that NP_{\_G47056}/NP_{\_G47132}=1
towards P_{\_G47056} N P_{\_G47132} 1 
cmark_r P_{\_G47056}
color 200 200 200
drawsegment N P_{\_G47056} 
color 0 0 0

% Constructing a point P_{\_G47101} such that NP_{\_G47101}/NP_{\_G47132}=3
towards P_{\_G47101} N P_{\_G47132} 3 
cmark_r P_{\_G47101}
color 200 200 200
drawsegment N P_{\_G47101} 
color 0 0 0

% Constructing a line L_{\_G47062} which passes through point O and point P_{\_G47101}
line L_{\_G47062} O P_{\_G47101} 

color 200 200 200
drawline L_{\_G47062}
color 0 0 0


% Constructing a line L_{\_G47025} which contains the point P_{\_G47056} and is parallel to the line L_{\_G47062}
parallel L_{\_G47025} P_{\_G47056} L_{\_G47062} 

color 200 200 200
drawline L_{\_G47025}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G47025} and line L_{\_G47031}
intersec G L_{\_G47025} L_{\_G47031} 
cmark_t G



% Constructing a point H such that NH/NO=-1
towards H N O -1 
cmark_rt H
color 200 200 200
drawsegment O H 
color 0 0 0


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

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



% NDG:  points H_{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 H_{b}
circle k(N,M_{a}) N H_{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 H_{b} and E_{b} must be different
% Constructing a point P_{\_G47959} which is a foot of the point N on the line h_{b}
foot P_{\_G47959} N h_{b} 
cmark_r P_{\_G47959}
color 200 200 200
drawline N P_{\_G47959} 
color 0 0 0

% Constructing a point E_{b} which is an image of the point H_{b} in the symmetry to point/line P_{\_G47959}
sim E_{b} P_{\_G47959} H_{b} 
cmark_r E_{b}



% 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 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 H_{b} and N are not the same
% Determination conditions:  points H_{b} and M_{b} are not the same; points H_{b} and E_{b} must be different; points H_{b} and H are not the same