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 H_{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[_G64102] with value 0.18420064727909524
number V[_G64102] 0.18420064727909524 


% Calculating value V[_G64123] using formula V[_G64102]*360
expression V[_G64123]  { V[_G64102]*360  } 


% Constructing a point H_{c} which is an image of the point V[_G64123] in a rotation around the point N for the angle E_{b}
rotate H_{c} N V[_G64123] E_{b} 
color 220 0 0
fontsize 11
cmark_lt H_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{b} V[_G64123] 
color 0 0 0


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

color 200 200 200
drawcircle k(E_{b},B)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(E_{b},B) intersect% DET:  circles k(N,M_{a}) and k(E_{b},B) are not the same; points H_{c} and H_{a} must be different
% Constructing a line L_{\_G64537} which passes through point N and point E_{b}
line L_{\_G64537} N E_{b} 

color 200 200 200
drawline L_{\_G64537}
color 0 0 0


% Constructing a point H_{a} which is an image of the point H_{c} in the symmetry to point/line L_{\_G64537}
sim H_{a} L_{\_G64537} H_{c} 
cmark_b H_{a}



% Generating number V[_G64639] with value 0.18420064727909524
number V[_G64639] 0.18420064727909524 


% Calculating value V[_G64660] using formula V[_G64639]*360
expression V[_G64660]  { V[_G64639]*360  } 


% Constructing a point A which is an image of the point V[_G64660] in a rotation around the point M_{b} for the angle H_{c}
rotate A M_{b} V[_G64660] H_{c} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{c} V[_G64660] 
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


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

color 200 200 200
drawline c
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



% NDG:  lines c and a are not parallel% DET:  lines c and a are not the same
% Constructing a point B which belongs to line c and line a
intersec B c a 
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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