Construction in GCLC language

dim 120 120

point H 80 72.73
point M_{b} 95 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H
cmark_rt M_{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_{\_G42246} which passes through point H and point N
line L_{\_G42246} H N 

color 200 200 200
drawline L_{\_G42246}
color 0 0 0


% Constructing a point P_{\_G42347} with coordinates (0,0)
point P_{\_G42347} 0 0 
cmark_r P_{\_G42347}

% Constructing a point P_{\_G42271} such that HP_{\_G42271}/HP_{\_G42347}=4
towards P_{\_G42271} H P_{\_G42347} 4 
cmark_r P_{\_G42271}
color 200 200 200
drawsegment H P_{\_G42271} 
color 0 0 0

% Constructing a point P_{\_G42316} such that HP_{\_G42316}/HP_{\_G42347}=3
towards P_{\_G42316} H P_{\_G42347} 3 
cmark_r P_{\_G42316}
color 200 200 200
drawsegment H P_{\_G42316} 
color 0 0 0

% Constructing a line L_{\_G42277} which passes through point N and point P_{\_G42316}
line L_{\_G42277} N P_{\_G42316} 

color 200 200 200
drawline L_{\_G42277}
color 0 0 0


% Constructing a line L_{\_G42240} which contains the point P_{\_G42271} and is parallel to the line L_{\_G42277}
parallel L_{\_G42240} P_{\_G42271} L_{\_G42277} 

color 200 200 200
drawline L_{\_G42240}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G42240} and line L_{\_G42246}
intersec G L_{\_G42240} L_{\_G42246} 
cmark_t G



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



% Constructing a point E_{b} such that HE_{b}/HB=0.5
towards E_{b} H B 0.5 
cmark_r E_{b}
color 200 200 200
drawsegment H B 
color 0 0 0


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

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



% NDG:  points M_{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 M_{b}
circle k(N,M_{a}) N M_{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 E_{b} and H_{b} must be different
% Constructing a point P_{\_G43257} which is a foot of the point N on the line h_{b}
foot P_{\_G43257} N h_{b} 
cmark_r P_{\_G43257}
color 200 200 200
drawline N P_{\_G43257} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point E_{b} in the symmetry to point/line P_{\_G43257}
sim H_{b} P_{\_G43257} E_{b} 
cmark_rt H_{b}


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