Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{b} 89.36 77.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_rt H_{b}
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_{\_G48461} which passes through point H and point N
line L_{\_G48461} H N 

color 200 200 200
drawline L_{\_G48461}
color 0 0 0


% Constructing a point P_{\_G48562} with coordinates (0,0)
point P_{\_G48562} 0 0 
cmark_r P_{\_G48562}

% Constructing a point P_{\_G48486} such that HP_{\_G48486}/HP_{\_G48562}=4
towards P_{\_G48486} H P_{\_G48562} 4 
cmark_r P_{\_G48486}
color 200 200 200
drawsegment H P_{\_G48486} 
color 0 0 0

% Constructing a point P_{\_G48531} such that HP_{\_G48531}/HP_{\_G48562}=3
towards P_{\_G48531} H P_{\_G48562} 3 
cmark_r P_{\_G48531}
color 200 200 200
drawsegment H P_{\_G48531} 
color 0 0 0

% Constructing a line L_{\_G48492} which passes through point N and point P_{\_G48531}
line L_{\_G48492} N P_{\_G48531} 

color 200 200 200
drawline L_{\_G48492}
color 0 0 0


% Constructing a line L_{\_G48455} which contains the point P_{\_G48486} and is parallel to the line L_{\_G48492}
parallel L_{\_G48455} P_{\_G48486} L_{\_G48492} 

color 200 200 200
drawline L_{\_G48455}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G48455} and line L_{\_G48461}
intersec G L_{\_G48455} L_{\_G48461} 
cmark_t G


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

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  points H_{b} 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_{b}
circle k(N,M_{a}) N H_{b} 

color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0



% NDG:  line h_{b} and circle k(N,M_{a}) intersect% DET:  points H_{b} and E_{b} must be different
% Constructing a point P_{\_G49315} which is a foot of the point N on the line h_{b}
foot P_{\_G49315} N h_{b} 
cmark_r P_{\_G49315}
color 200 200 200
drawline N P_{\_G49315} 
color 0 0 0

% Constructing a point E_{b} which is an image of the point H_{b} in the symmetry to point/line P_{\_G49315}
sim E_{b} P_{\_G49315} H_{b} 
cmark_r E_{b}



% Constructing a point B such that E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0



% Constructing a point M_{b} such that GM_{b}/GB=-0.5
towards M_{b} G B -0.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
color 0 0 0


% DET:  points H_{b} and M_{b} are not the same
% Constructing a line b which passes through point H_{b} and point M_{b}
line b H_{b} M_{b} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  points B and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point B
circle k(O,C) O B 

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line b and circle k(O,C) intersect
% Constructing points C and A which are in intersection of k(O,C) and b
intersec2 C A k(O,C) b 
cmark_b C
cmark_t A



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line b and circle k(O,C) intersect; points B and O are not the same; line h_{b} and circle k(N,M_{a}) intersect; points H_{b} and N are not the same
% Determination conditions:  points H_{b} and M_{b} are not the same; points H_{b} and E_{b} must be different; points H and H_{b} are not the same