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 H_{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[_G40510] with value 0.8744309729437407
number V[_G40510] 0.8744309729437407 


% Calculating value V[_G40531] using formula V[_G40510]*360
expression V[_G40531]  { V[_G40510]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G40531] in a rotation around the point N for the angle E_{c}
rotate H_{a} N V[_G40531] E_{c} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{c} V[_G40531] 
color 0 0 0


% NDG:  points H_{a} and E_{c} are not the same
% Constructing a circle k(E_{c},C) whose center is at point E_{c} and which passes through point H_{a}
circle k(E_{c},C) E_{c} H_{a} 

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(E_{c},C) intersect% DET:  circles k(N,M_{a}) and k(E_{c},C) are not the same; points H_{a} and H_{b} must be different
% Constructing a line L_{\_G40945} which passes through point N and point E_{c}
line L_{\_G40945} N E_{c} 

color 200 200 200
drawline L_{\_G40945}
color 0 0 0


% Constructing a point H_{b} which is an image of the point H_{a} in the symmetry to point/line L_{\_G40945}
sim H_{b} L_{\_G40945} H_{a} 
cmark_rt H_{b}



% Generating number V[_G41047] with value 0.8744309729437407
number V[_G41047] 0.8744309729437407 


% Calculating value V[_G41068] using formula V[_G41047]*360
expression V[_G41068]  { V[_G41047]*360  } 


% Constructing a point A which is an image of the point V[_G41068] in a rotation around the point M_{c} for the angle H_{a}
rotate A M_{c} V[_G41068] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{a} V[_G41068] 
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


% DET:  points A and H_{a} are not the same
% Constructing a line h_{a} which passes through point A and point H_{a}
line h_{a} A H_{a} 

color 200 200 200
drawline h_{a}
color 0 0 0



% DET:  points H_{b} and B are not the same
% Constructing a line h_{b} which passes through point H_{b} and point B
line h_{b} H_{b} B 

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  lines h_{a} and h_{b} are not parallel% DET:  lines h_{a} and h_{b} are not the same
% Constructing a point H which belongs to line h_{a} and line h_{b}
intersec H h_{a} h_{b} 
cmark_rt H



% 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:  lines h_{a} and h_{b} are not parallel; circles k(N,M_{a}) and k(E_{c},C) intersect; points H_{a} and E_{c} are not the same; 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 h_{a} and h_{b} are not the same; points H_{b} and B are not the same; points A and H_{a} are not the same; circles k(N,M_{a}) and k(E_{c},C) are not the same; points H_{a} and H_{b} must be different; 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