Construction in GCLC language

dim 120 120

point G 70 58.33
point M_{c} 50 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_t G
cmark_lt M_{c}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point C such that GC/GM_{c}=-2
towards C G M_{c} -2 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



% Constructing a point H such that GH/GN=4
towards H G N 4 
cmark_rt H
color 200 200 200
drawsegment G H 
color 0 0 0



% Constructing a point O such that GO/GN=-2
towards O G N -2 
cmark_t O
color 200 200 200
drawsegment N O 
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 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_{\_G48790} which is a foot of the point N on the line h_{c}
foot P_{\_G48790} N h_{c} 
cmark_r P_{\_G48790}
color 200 200 200
drawline N P_{\_G48790} 
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_{\_G48790}
sim H_{c} P_{\_G48790} 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 M_{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 C and H are not the same