Construction in GCLC language

dim 120 120

point H_{a} 80 40
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_b H_{a}
cmark_r N
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 
% NDG:  points H_{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 H_{a}
circle k(N,M_{a}) N H_{a} 

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




% Generating number V[_G58577] with value 0.2816678668055405
number V[_G58577] 0.2816678668055405 


% Calculating value V[_G58598] using formula V[_G58577]*360
expression V[_G58598]  { V[_G58577]*360  } 


% Constructing a point E_{c} which is an image of the point V[_G58598] in a rotation around the point N for the angle H_{a}
rotate E_{c} N V[_G58598] H_{a} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{a} V[_G58598] 
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}


% 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_{\_G59192} which passes through point N and point E_{c}
line L_{\_G59192} N E_{c} 

color 200 200 200
drawline L_{\_G59192}
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_{\_G59192}
sim H_{b} L_{\_G59192} H_{a} 
cmark_rt H_{b}



% Generating number V[_G59294] with value 0.2816678668055405
number V[_G59294] 0.2816678668055405 


% Calculating value V[_G59315] using formula V[_G59294]*360
expression V[_G59315]  { V[_G59294]*360  } 


% Constructing a point A which is an image of the point V[_G59315] in a rotation around the point M_{c} for the angle H_{a}
rotate A M_{c} V[_G59315] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{a} V[_G59315] 
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; line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; points H_{a} and N are not the same
% 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; points E_{c} and M_{c} must be different; points E_{c} and N are not the same