Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b M_{a}
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_{a} and M_{a} are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point E_{a} and point M_{a}
line m(H_{b}H_{c}) E_{a} M_{a} 

color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0



% DET:  points E_{a} and M_{a} are not the same
% Constructing bisector m(E_{a}M_{a}) of the segment E_{a}M_{a}
med m(E_{a}M_{a}) E_{a} M_{a} 

color 200 200 200
drawline m(E_{a}M_{a})
color 0 0 0

color 200 200 200
drawsegment E_{a} M_{a} 
color 0 0 0


% NDG:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel% DET:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{a}M_{a}) and line m(H_{b}H_{c})
intersec N m(E_{a}M_{a}) m(H_{b}H_{c}) 
cmark_r N


% NDG:  points E_{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 E_{a}
circle k(N,M_{a}) N E_{a} 

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




% Generating number V[_G58367] with value 0.652776598416338
number V[_G58367] 0.652776598416338 


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


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

color 200 200 200
drawarc_p N E_{a} V[_G58388] 
color 0 0 0


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

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(E_{a},A) intersect% DET:  circles k(N,M_{a}) and k(E_{a},A) are not the same; points H_{c} and H_{b} must be different
% Constructing a line L_{\_G58802} which passes through point N and point E_{a}
line L_{\_G58802} N E_{a} 

color 200 200 200
drawline L_{\_G58802}
color 0 0 0


% Constructing a point H_{b} which is an image of the point H_{c} in the symmetry to point/line L_{\_G58802}
sim H_{b} L_{\_G58802} H_{c} 
cmark_rt H_{b}



% Generating number V[_G58904] with value 0.652776598416338
number V[_G58904] 0.652776598416338 


% Calculating value V[_G58925] using formula V[_G58904]*360
expression V[_G58925]  { V[_G58904]*360  } 


% Constructing a point A which is an image of the point V[_G58925] in a rotation around the point E_{a} for the angle H_{c}
rotate A E_{a} V[_G58925] H_{c} 
cmark_t A
color 200 200 200
drawarc_p E_{a} H_{c} V[_G58925] 
color 0 0 0



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
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_{b} and H are not the same
% Constructing a line h_{b} which passes through point H_{b} and point H
line h_{b} H_{b} H 

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



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



% Constructing a point C such that M_{a}C/M_{a}B=-1
towards C M_{a} B -1 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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