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 E_{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[_G27708] with value 0.9347308639608486
number V[_G27708] 0.9347308639608486 


% Calculating value V[_G27729] using formula V[_G27708]*360
expression V[_G27729]  { V[_G27708]*360  } 


% Constructing a point E_{b} which is an image of the point V[_G27729] in a rotation around the point N for the angle E_{a}
rotate E_{b} N V[_G27729] E_{a} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{a} V[_G27729] 
color 0 0 0


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

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



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



% Constructing a free point A
point A 80 95

cmark_t A



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0



% 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 E_{b}B/E_{b}H=-1
towards B E_{b} H -1 
cmark_b B
color 200 200 200
drawsegment H B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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