Construction in GCLC language

dim 120 120

point C 110 40
point E_{c} 95 56.36
point M_{c} 50 67.5

color 220 0 0
fontsize 11

cmark_b C
cmark_r E_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10


% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0



% Constructing a line L_{\_G30392} which passes through point C and point M_{c}
line L_{\_G30392} C M_{c} 

color 200 200 200
drawline L_{\_G30392}
color 0 0 0


% Constructing a point P_{\_G30493} with coordinates (0,0)
point P_{\_G30493} 0 0 
cmark_r P_{\_G30493}

% Constructing a point P_{\_G30417} such that CP_{\_G30417}/CP_{\_G30493}=2
towards P_{\_G30417} C P_{\_G30493} 2 
cmark_r P_{\_G30417}
color 200 200 200
drawsegment C P_{\_G30417} 
color 0 0 0

% Constructing a point P_{\_G30462} such that CP_{\_G30462}/CP_{\_G30493}=3
towards P_{\_G30462} C P_{\_G30493} 3 
cmark_r P_{\_G30462}
color 200 200 200
drawsegment C P_{\_G30462} 
color 0 0 0

% Constructing a line L_{\_G30423} which passes through point M_{c} and point P_{\_G30462}
line L_{\_G30423} M_{c} P_{\_G30462} 

color 200 200 200
drawline L_{\_G30423}
color 0 0 0


% Constructing a line L_{\_G30386} which contains the point P_{\_G30417} and is parallel to the line L_{\_G30423}
parallel L_{\_G30386} P_{\_G30417} L_{\_G30423} 

color 200 200 200
drawline L_{\_G30386}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G30386} and line L_{\_G30392}
intersec G L_{\_G30386} L_{\_G30392} 
cmark_t G



% Constructing a point N such that HN/HG=0.75
towards N H G 0.75 
cmark_r N
color 200 200 200
drawsegment H G 
color 0 0 0



% Constructing a point O such that HO/HG=1.5
towards O H G 1.5 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


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

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 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_{\_G31463} which is a foot of the point N on the line h_{c}
foot P_{\_G31463} N h_{c} 
cmark_r P_{\_G31463}
color 200 200 200
drawline N P_{\_G31463} 
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_{\_G31463}
sim H_{c} P_{\_G31463} 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 E_{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 E_{c} are not the same