Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b M_{a}
color 0 0 0
fontsize 10


% point M_{b} is given by the problem setting, but it has to belong to the circle k(N,M_{a}) which is constructible from the others objects given 
% DET:  points E_{a} and M_{a} are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point E_{a} and point M_{a}
line m(H_{b}H_{c}) E_{a} M_{a} 

color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0



% DET:  points E_{a} and M_{a} are not the same
% Constructing bisector m(E_{a}M_{a}) of the segment E_{a}M_{a}
med m(E_{a}M_{a}) E_{a} M_{a} 

color 200 200 200
drawline m(E_{a}M_{a})
color 0 0 0

color 200 200 200
drawsegment E_{a} M_{a} 
color 0 0 0


% NDG:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel% DET:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{a}M_{a}) and line m(H_{b}H_{c})
intersec N m(E_{a}M_{a}) m(H_{b}H_{c}) 
cmark_r N


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

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




% Generating number V[_G54554] with value 0.6859827355848878
number V[_G54554] 0.6859827355848878 


% Calculating value V[_G54575] using formula V[_G54554]*360
expression V[_G54575]  { V[_G54554]*360  } 


% Constructing a point M_{b} which is an image of the point V[_G54575] in a rotation around the point N for the angle E_{a}
rotate M_{b} N V[_G54575] E_{a} 
color 220 0 0
fontsize 11
cmark_rt M_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{a} V[_G54575] 
color 0 0 0



% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
color 0 0 0



% Constructing a line L_{\_G54878} which passes through point A and point M_{a}
line L_{\_G54878} A M_{a} 

color 200 200 200
drawline L_{\_G54878}
color 0 0 0


% Constructing a point P_{\_G54979} with coordinates (0,0)
point P_{\_G54979} 0 0 
cmark_r P_{\_G54979}

% Constructing a point P_{\_G54903} such that AP_{\_G54903}/AP_{\_G54979}=2
towards P_{\_G54903} A P_{\_G54979} 2 
cmark_r P_{\_G54903}
color 200 200 200
drawsegment A P_{\_G54903} 
color 0 0 0

% Constructing a point P_{\_G54948} such that AP_{\_G54948}/AP_{\_G54979}=3
towards P_{\_G54948} A P_{\_G54979} 3 
cmark_r P_{\_G54948}
color 200 200 200
drawsegment A P_{\_G54948} 
color 0 0 0

% Constructing a line L_{\_G54909} which passes through point M_{a} and point P_{\_G54948}
line L_{\_G54909} M_{a} P_{\_G54948} 

color 200 200 200
drawline L_{\_G54909}
color 0 0 0


% Constructing a line L_{\_G54872} which contains the point P_{\_G54903} and is parallel to the line L_{\_G54909}
parallel L_{\_G54872} P_{\_G54903} L_{\_G54909} 

color 200 200 200
drawline L_{\_G54872}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G54872} and line L_{\_G54878}
intersec G L_{\_G54872} L_{\_G54878} 
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



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  points E_{a} and N are not the same; lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel
% Determination conditions:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same; points E_{a} and M_{a} are not the same; points E_{a} and M_{a} are not the same