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 E_{c} 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[_G62710] with value 0.5032901031629208
number V[_G62710] 0.5032901031629208 


% Calculating value V[_G62731] using formula V[_G62710]*360
expression V[_G62731]  { V[_G62710]*360  } 


% Constructing a point E_{c} which is an image of the point V[_G62731] in a rotation around the point N for the angle E_{b}
rotate E_{c} N V[_G62731] E_{b} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{b} V[_G62731] 
color 0 0 0


% DET:  points E_{c} and N are not the same
% Constructing a line m(H_{b}H_{a}) which passes through point E_{c} and point N
line m(H_{b}H_{a}) E_{c} N 

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



% NDG:  line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect% DET:  points E_{c} and M_{c} must be different
% Constructing a point M_{c} which is an image of the point E_{c} in the symmetry to point/line N
sim M_{c} N E_{c} 
cmark_lt M_{c}



% 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 AB/AM_{c}=2
towards B A M_{c} 2 
cmark_b B
color 200 200 200
drawsegment A B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; 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:  points E_{c} and M_{c} must be different; points E_{c} and N are not the same; 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