Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{c} 68.91 84.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_lt H_{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_{\_G44899} which passes through point H and point N
line L_{\_G44899} H N 

color 200 200 200
drawline L_{\_G44899}
color 0 0 0


% Constructing a point P_{\_G45000} with coordinates (0,0)
point P_{\_G45000} 0 0 
cmark_r P_{\_G45000}

% Constructing a point P_{\_G44924} such that HP_{\_G44924}/HP_{\_G45000}=4
towards P_{\_G44924} H P_{\_G45000} 4 
cmark_r P_{\_G44924}
color 200 200 200
drawsegment H P_{\_G44924} 
color 0 0 0

% Constructing a point P_{\_G44969} such that HP_{\_G44969}/HP_{\_G45000}=3
towards P_{\_G44969} H P_{\_G45000} 3 
cmark_r P_{\_G44969}
color 200 200 200
drawsegment H P_{\_G44969} 
color 0 0 0

% Constructing a line L_{\_G44930} which passes through point N and point P_{\_G44969}
line L_{\_G44930} N P_{\_G44969} 

color 200 200 200
drawline L_{\_G44930}
color 0 0 0


% Constructing a line L_{\_G44893} which contains the point P_{\_G44924} and is parallel to the line L_{\_G44930}
parallel L_{\_G44893} P_{\_G44924} L_{\_G44930} 

color 200 200 200
drawline L_{\_G44893}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G44893} and line L_{\_G44899}
intersec G L_{\_G44893} L_{\_G44899} 
cmark_t G


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

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



% NDG:  points H_{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 H_{c}
circle k(N,M_{a}) N H_{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 H_{c} and E_{c} must be different
% Constructing a point P_{\_G45753} which is a foot of the point N on the line h_{c}
foot P_{\_G45753} N h_{c} 
cmark_r P_{\_G45753}
color 200 200 200
drawline N P_{\_G45753} 
color 0 0 0

% Constructing a point E_{c} which is an image of the point H_{c} in the symmetry to point/line P_{\_G45753}
sim E_{c} P_{\_G45753} H_{c} 
cmark_r E_{c}



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