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_{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_{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[_G52886] with value 0.6967366903847217
number V[_G52886] 0.6967366903847217 


% Calculating value V[_G52907] using formula V[_G52886]*360
expression V[_G52907]  { V[_G52886]*360  } 


% Constructing a point E_{b} which is an image of the point V[_G52907] in a rotation around the point N for the angle H_{b}
rotate E_{b} N V[_G52907] H_{b} 
color 220 0 0
fontsize 11
cmark_r E_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{b} V[_G52907] 
color 0 0 0


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

color 200 200 200
drawline h_{b}
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}


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

color 200 200 200
drawline b
color 0 0 0




% Constructing a point A such that H_{b}A/H_{b}M_{b}=0.6967366903847217
towards A H_{b} M_{b} 0.6967366903847217 
cmark_t A
color 200 200 200
drawsegment H_{b} M_{b} 
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


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

color 200 200 200
drawcircle k(M_{b},C)
color 0 0 0



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


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