Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H_{b}
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_{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 H_{b}
circle k(N,M_{a}) N H_{b} 

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




% Generating number V[_G54502] with value 0.13797950779540158
number V[_G54502] 0.13797950779540158 


% Calculating value V[_G54523] using formula V[_G54502]*360
expression V[_G54523]  { V[_G54502]*360  } 


% Constructing a point E_{c} which is an image of the point V[_G54523] in a rotation around the point N for the angle H_{b}
rotate E_{c} N V[_G54523] H_{b} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{b} V[_G54523] 
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_{b} 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_{b}
circle k(E_{c},C) E_{c} H_{b} 

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_{b} and H_{a} must be different
% Constructing a line L_{\_G55117} which passes through point N and point E_{c}
line L_{\_G55117} N E_{c} 

color 200 200 200
drawline L_{\_G55117}
color 0 0 0


% Constructing a point H_{a} which is an image of the point H_{b} in the symmetry to point/line L_{\_G55117}
sim H_{a} L_{\_G55117} H_{b} 
cmark_b H_{a}



% Generating number V[_G55219] with value 0.13797950779540158
number V[_G55219] 0.13797950779540158 


% Calculating value V[_G55240] using formula V[_G55219]*360
expression V[_G55240]  { V[_G55219]*360  } 


% Constructing a point A which is an image of the point V[_G55240] in a rotation around the point M_{c} for the angle H_{b}
rotate A M_{c} V[_G55240] H_{b} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{b} V[_G55240] 
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_{b} are not the same
% Constructing a line b which passes through point A and point H_{b}
line b A H_{b} 

color 200 200 200
drawline b
color 0 0 0



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

color 200 200 200
drawline a
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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