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_{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 
% 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[_G58367] with value 0.16461259377723547
number V[_G58367] 0.16461259377723547 


% Calculating value V[_G58388] using formula V[_G58367]*360
expression V[_G58388]  { V[_G58367]*360  } 


% Constructing a point E_{b} which is an image of the point V[_G58388] in a rotation around the point N for the angle H_{a}
rotate E_{b} N V[_G58388] H_{a} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{a} V[_G58388] 
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}


% NDG:  points H_{a} 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_{a}
circle k(E_{b},B) E_{b} H_{a} 

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_{a} and H_{c} must be different
% Constructing a line L_{\_G58982} which passes through point N and point E_{b}
line L_{\_G58982} N E_{b} 

color 200 200 200
drawline L_{\_G58982}
color 0 0 0


% Constructing a point H_{c} which is an image of the point H_{a} in the symmetry to point/line L_{\_G58982}
sim H_{c} L_{\_G58982} H_{a} 
cmark_lt H_{c}



% Generating number V[_G59084] with value 0.16461259377723547
number V[_G59084] 0.16461259377723547 


% Calculating value V[_G59105] using formula V[_G59084]*360
expression V[_G59105]  { V[_G59084]*360  } 


% Constructing a point A which is an image of the point V[_G59105] in a rotation around the point M_{b} for the angle H_{a}
rotate A M_{b} V[_G59105] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{a} V[_G59105] 
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_{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_{c} and C are not the same
% Constructing a line h_{c} which passes through point H_{c} and point C
line h_{c} H_{c} C 

color 200 200 200
drawline h_{c}
color 0 0 0



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



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