Construction in GCLC language

dim 120 120

point H 80 72.73
point M_{c} 50 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_lt M_{c}
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point O such that HO/HN=2
towards O H N 2 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0



% Constructing a line L_{\_G61429} which passes through point H and point N
line L_{\_G61429} H N 

color 200 200 200
drawline L_{\_G61429}
color 0 0 0


% Constructing a point P_{\_G61530} with coordinates (0,0)
point P_{\_G61530} 0 0 
cmark_r P_{\_G61530}

% Constructing a point P_{\_G61454} such that HP_{\_G61454}/HP_{\_G61530}=4
towards P_{\_G61454} H P_{\_G61530} 4 
cmark_r P_{\_G61454}
color 200 200 200
drawsegment H P_{\_G61454} 
color 0 0 0

% Constructing a point P_{\_G61499} such that HP_{\_G61499}/HP_{\_G61530}=3
towards P_{\_G61499} H P_{\_G61530} 3 
cmark_r P_{\_G61499}
color 200 200 200
drawsegment H P_{\_G61499} 
color 0 0 0

% Constructing a line L_{\_G61460} which passes through point N and point P_{\_G61499}
line L_{\_G61460} N P_{\_G61499} 

color 200 200 200
drawline L_{\_G61460}
color 0 0 0


% Constructing a line L_{\_G61423} which contains the point P_{\_G61454} and is parallel to the line L_{\_G61460}
parallel L_{\_G61423} P_{\_G61454} L_{\_G61460} 

color 200 200 200
drawline L_{\_G61423}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G61423} and line L_{\_G61429}
intersec G L_{\_G61423} L_{\_G61429} 
cmark_t G



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
color 0 0 0



% Constructing a point E_{c} such that HE_{c}/HC=0.5
towards E_{c} H C 0.5 
cmark_r E_{c}
color 200 200 200
drawsegment H C 
color 0 0 0


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

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_{\_G62440} which is a foot of the point N on the line h_{c}
foot P_{\_G62440} N h_{c} 
cmark_r P_{\_G62440}
color 200 200 200
drawline N P_{\_G62440} 
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_{\_G62440}
sim H_{c} P_{\_G62440} 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 H and C are not the same