Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G56728} which passes through point N and point O
line L_{\_G56728} N O 

color 200 200 200
drawline L_{\_G56728}
color 0 0 0


% Constructing a point P_{\_G56829} with coordinates (0,0)
point P_{\_G56829} 0 0 
cmark_r P_{\_G56829}

% Constructing a point P_{\_G56753} such that NP_{\_G56753}/NP_{\_G56829}=1
towards P_{\_G56753} N P_{\_G56829} 1 
cmark_r P_{\_G56753}
color 200 200 200
drawsegment N P_{\_G56753} 
color 0 0 0

% Constructing a point P_{\_G56798} such that NP_{\_G56798}/NP_{\_G56829}=3
towards P_{\_G56798} N P_{\_G56829} 3 
cmark_r P_{\_G56798}
color 200 200 200
drawsegment N P_{\_G56798} 
color 0 0 0

% Constructing a line L_{\_G56759} which passes through point O and point P_{\_G56798}
line L_{\_G56759} O P_{\_G56798} 

color 200 200 200
drawline L_{\_G56759}
color 0 0 0


% Constructing a line L_{\_G56722} which contains the point P_{\_G56753} and is parallel to the line L_{\_G56759}
parallel L_{\_G56722} P_{\_G56753} L_{\_G56759} 

color 200 200 200
drawline L_{\_G56722}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G56722} and line L_{\_G56728}
intersec G L_{\_G56722} L_{\_G56728} 
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



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

color 200 200 200
drawline h_{c}
color 0 0 0



% NDG:  points E_{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 E_{c}
circle k(N,M_{a}) N E_{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 E_{c} and H_{c} must be different
% Constructing a point P_{\_G57813} which is a foot of the point N on the line h_{c}
foot P_{\_G57813} N h_{c} 
cmark_r P_{\_G57813}
color 200 200 200
drawline N P_{\_G57813} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point E_{c} in the symmetry to point/line P_{\_G57813}
sim H_{c} P_{\_G57813} E_{c} 
cmark_lt H_{c}


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