Construction in GCLC language

dim 120 120

point C 110 40
point N 72.5 61.93
point O 65 51.14

color 220 0 0
fontsize 11

cmark_b C
cmark_r N
cmark_t O
color 0 0 0
fontsize 10


% Constructing a line L_{\_G25730} which passes through point N and point O
line L_{\_G25730} N O 

color 200 200 200
drawline L_{\_G25730}
color 0 0 0


% Constructing a point P_{\_G25831} with coordinates (0,0)
point P_{\_G25831} 0 0 
cmark_r P_{\_G25831}

% Constructing a point P_{\_G25755} such that NP_{\_G25755}/NP_{\_G25831}=1
towards P_{\_G25755} N P_{\_G25831} 1 
cmark_r P_{\_G25755}
color 200 200 200
drawsegment N P_{\_G25755} 
color 0 0 0

% Constructing a point P_{\_G25800} such that NP_{\_G25800}/NP_{\_G25831}=3
towards P_{\_G25800} N P_{\_G25831} 3 
cmark_r P_{\_G25800}
color 200 200 200
drawsegment N P_{\_G25800} 
color 0 0 0

% Constructing a line L_{\_G25761} which passes through point O and point P_{\_G25800}
line L_{\_G25761} O P_{\_G25800} 

color 200 200 200
drawline L_{\_G25761}
color 0 0 0


% Constructing a line L_{\_G25724} which contains the point P_{\_G25755} and is parallel to the line L_{\_G25761}
parallel L_{\_G25724} P_{\_G25755} L_{\_G25761} 

color 200 200 200
drawline L_{\_G25724}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G25724} and line L_{\_G25730}
intersec G L_{\_G25724} L_{\_G25730} 
cmark_t G



% Constructing a point M_{c} such that CM_{c}/CG=1.5
towards M_{c} C G 1.5 
cmark_lt M_{c}
color 200 200 200
drawsegment C M_{c} 
color 0 0 0



% 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 E_{c} such that CE_{c}/CH=0.5
towards E_{c} C H 0.5 
cmark_r E_{c}
color 200 200 200
drawsegment C H 
color 0 0 0


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

color 200 200 200
drawline h_{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:  points M_{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 M_{c}
circle k(N,M_{a}) N M_{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_{\_G26875} which is a foot of the point N on the line h_{c}
foot P_{\_G26875} N h_{c} 
cmark_r P_{\_G26875}
color 200 200 200
drawline N P_{\_G26875} 
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_{\_G26875}
sim H_{c} P_{\_G26875} 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:  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; line h_{c} and circle k(N,M_{a}) intersect; points M_{c} and N are not the same; points C and O 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 C and H are not the same