Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_lt H_{c}
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G73637} which passes through point N and point O
line L_{\_G73637} N O 

color 200 200 200
drawline L_{\_G73637}
color 0 0 0


% Constructing a point P_{\_G73738} with coordinates (0,0)
point P_{\_G73738} 0 0 
cmark_r P_{\_G73738}

% Constructing a point P_{\_G73662} such that NP_{\_G73662}/NP_{\_G73738}=1
towards P_{\_G73662} N P_{\_G73738} 1 
cmark_r P_{\_G73662}
color 200 200 200
drawsegment N P_{\_G73662} 
color 0 0 0

% Constructing a point P_{\_G73707} such that NP_{\_G73707}/NP_{\_G73738}=3
towards P_{\_G73707} N P_{\_G73738} 3 
cmark_r P_{\_G73707}
color 200 200 200
drawsegment N P_{\_G73707} 
color 0 0 0

% Constructing a line L_{\_G73668} which passes through point O and point P_{\_G73707}
line L_{\_G73668} O P_{\_G73707} 

color 200 200 200
drawline L_{\_G73668}
color 0 0 0


% Constructing a line L_{\_G73631} which contains the point P_{\_G73662} and is parallel to the line L_{\_G73668}
parallel L_{\_G73631} P_{\_G73662} L_{\_G73668} 

color 200 200 200
drawline L_{\_G73631}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G73631} and line L_{\_G73637}
intersec G L_{\_G73631} L_{\_G73637} 
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_{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:  points H_{c} 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_{c}
circle k(N,M_{a}) N H_{c} 

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



% NDG:  line h_{c} and circle k(N,M_{a}) intersect% DET:  points H_{c} and E_{c} must be different
% Constructing a point P_{\_G74565} which is a foot of the point N on the line h_{c}
foot P_{\_G74565} N h_{c} 
cmark_r P_{\_G74565}
color 200 200 200
drawline N P_{\_G74565} 
color 0 0 0

% Constructing a point E_{c} which is an image of the point H_{c} in the symmetry to point/line P_{\_G74565}
sim E_{c} P_{\_G74565} H_{c} 
cmark_r E_{c}



% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



% Constructing a point M_{c} such that GM_{c}/GC=-0.5
towards M_{c} G C -0.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c} 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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