Construction in GCLC language

dim 120 120

point E_{b} 50 56.36
point M_{b} 95 67.5

color 220 0 0
fontsize 11

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


% point M_{a} 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_{b} and M_{b} are not the same
% Constructing a line m(H_{a}H_{c}) which passes through point E_{b} and point M_{b}
line m(H_{a}H_{c}) E_{b} M_{b} 

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



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

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

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


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


% 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




% Generating number V[_G54015] with value 0.32381110192415685
number V[_G54015] 0.32381110192415685 


% Calculating value V[_G54036] using formula V[_G54015]*360
expression V[_G54036]  { V[_G54015]*360  } 


% Constructing a point M_{a} which is an image of the point V[_G54036] in a rotation around the point N for the angle E_{b}
rotate M_{a} N V[_G54036] E_{b} 
color 220 0 0
fontsize 11
cmark_b M_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{b} V[_G54036] 
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 point B such that M_{a}B/M_{a}C=-1
towards B M_{a} C -1 
cmark_b B
color 200 200 200
drawsegment C B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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