Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_lt H_{c}
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_{c} 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_{c}
circle k(N,M_{a}) N H_{c} 

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




% Generating number V[_G64780] with value 0.6486868022905022
number V[_G64780] 0.6486868022905022 


% Calculating value V[_G64801] using formula V[_G64780]*360
expression V[_G64801]  { V[_G64780]*360  } 


% Constructing a point E_{c} which is an image of the point V[_G64801] in a rotation around the point N for the angle H_{c}
rotate E_{c} N V[_G64801] H_{c} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{c} V[_G64801] 
color 0 0 0


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

color 200 200 200
drawline h_{c}
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}


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

color 200 200 200
drawline c
color 0 0 0




% Constructing a point A such that H_{c}A/H_{c}M_{c}=0.6486868022905022
towards A H_{c} M_{c} 0.6486868022905022 
cmark_t A
color 200 200 200
drawsegment H_{c} M_{c} 
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


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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



% NDG:  circles k(N,M_{a}) and k(M_{c},A) intersect% DET:  circles k(N,M_{a}) and k(M_{c},A) are not the same
% Constructing points H_{a} and H_{b} which are in intersection of k(N,M_{a}) and k(M_{c},A)
intersec2 H_{a} H_{b} k(N,M_{a}) k(M_{c},A) 
cmark_b H_{a}
cmark_rt H_{b}


% 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



% NDG:  lines h_{c} and h_{a} are not parallel% DET:  lines h_{c} and h_{a} are not the same
% Constructing a point H which belongs to line h_{c} and line h_{a}
intersec H h_{c} h_{a} 
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_{c} and h_{a} are not parallel; circles k(N,M_{a}) and k(M_{c},A) intersect; points A and M_{c} are not the same; line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; points H_{c} and N are not the same
% Determination conditions:  lines h_{c} and h_{a} are not the same; points A and H_{a} are not the same; circles k(N,M_{a}) and k(M_{c},A) are not the same; points M_{c} and H_{c} are not the same; points E_{c} and M_{c} must be different; points E_{c} and N are not the same; points E_{c} and H_{c} are not the same