Construction in GCLC language

dim 120 120

point B 20 40
point E_{b} 50 56.36
point M_{b} 95 67.5

color 220 0 0
fontsize 11

cmark_b B
cmark_r E_{b}
cmark_rt M_{b}
color 0 0 0
fontsize 10


% Constructing a point H such that BH/BE_{b}=2
towards H B E_{b} 2 
cmark_rt H
color 200 200 200
drawsegment B H 
color 0 0 0



% Constructing a line L_{\_G20241} which passes through point B and point M_{b}
line L_{\_G20241} B M_{b} 

color 200 200 200
drawline L_{\_G20241}
color 0 0 0


% Constructing a point P_{\_G20342} with coordinates (0,0)
point P_{\_G20342} 0 0 
cmark_r P_{\_G20342}

% Constructing a point P_{\_G20266} such that BP_{\_G20266}/BP_{\_G20342}=2
towards P_{\_G20266} B P_{\_G20342} 2 
cmark_r P_{\_G20266}
color 200 200 200
drawsegment B P_{\_G20266} 
color 0 0 0

% Constructing a point P_{\_G20311} such that BP_{\_G20311}/BP_{\_G20342}=3
towards P_{\_G20311} B P_{\_G20342} 3 
cmark_r P_{\_G20311}
color 200 200 200
drawsegment B P_{\_G20311} 
color 0 0 0

% Constructing a line L_{\_G20272} which passes through point M_{b} and point P_{\_G20311}
line L_{\_G20272} M_{b} P_{\_G20311} 

color 200 200 200
drawline L_{\_G20272}
color 0 0 0


% Constructing a line L_{\_G20235} which contains the point P_{\_G20266} and is parallel to the line L_{\_G20272}
parallel L_{\_G20235} P_{\_G20266} L_{\_G20272} 

color 200 200 200
drawline L_{\_G20235}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G20235} and line L_{\_G20241}
intersec G L_{\_G20235} L_{\_G20241} 
cmark_t G



% Constructing a point N such that HN/HG=0.75
towards N H G 0.75 
cmark_r N
color 200 200 200
drawsegment H G 
color 0 0 0



% Constructing a point O such that HO/HG=1.5
towards O H G 1.5 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


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

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 E_{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 E_{b}
circle k(N,M_{a}) N E_{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_{\_G21312} which is a foot of the point N on the line h_{b}
foot P_{\_G21312} N h_{b} 
cmark_r P_{\_G21312}
color 200 200 200
drawline N P_{\_G21312} 
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_{\_G21312}
sim H_{b} P_{\_G21312} 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 E_{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 E_{b} are not the same