Construction in GCLC language

dim 120 120

point B 20 40
point G 70 58.33
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b B
cmark_t G
cmark_r N
color 0 0 0
fontsize 10


% Constructing a point M_{b} such that BM_{b}/BG=1.5
towards M_{b} B G 1.5 
cmark_rt M_{b}
color 200 200 200
drawsegment B M_{b} 
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 E_{b} such that BE_{b}/BH=0.5
towards E_{b} B H 0.5 
cmark_r E_{b}
color 200 200 200
drawsegment B 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


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

color 200 200 200
drawline h_{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:  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_{\_G28297} which is a foot of the point N on the line h_{b}
foot P_{\_G28297} N h_{b} 
cmark_r P_{\_G28297}
color 200 200 200
drawline N P_{\_G28297} 
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_{\_G28297}
sim H_{b} P_{\_G28297} 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:  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; line h_{b} and circle k(N,M_{a}) intersect; points M_{b} and N are not the same; points B and O 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 B and H are not the same