Construction in GCLC language

dim 120 120

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

color 220 0 0
fontsize 11

cmark_r E_{c}
cmark_lt M_{c}
color 0 0 0
fontsize 10


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

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



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

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

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


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


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

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




% Generating number V[_G28262] with value 0.7040315086355295
number V[_G28262] 0.7040315086355295 


% Calculating value V[_G28283] using formula V[_G28262]*360
expression V[_G28283]  { V[_G28262]*360  } 


% Constructing a point E_{a} which is an image of the point V[_G28283] in a rotation around the point N for the angle E_{c}
rotate E_{a} N V[_G28283] E_{c} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{c} V[_G28283] 
color 0 0 0



% 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 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



% Constructing a point C such that E_{c}C/E_{c}H=-1
towards C E_{c} H -1 
cmark_b C
color 200 200 200
drawsegment H C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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