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_{a} 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[_G29039] with value 0.7876223686239064
number V[_G29039] 0.7876223686239064 


% Calculating value V[_G29060] using formula V[_G29039]*360
expression V[_G29060]  { V[_G29039]*360  } 


% Constructing a point E_{a} which is an image of the point V[_G29060] in a rotation around the point N for the angle H_{a}
rotate E_{a} N V[_G29060] H_{a} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{a} V[_G29060] 
color 0 0 0


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

color 200 200 200
drawline h_{a}
color 0 0 0



% DET:  points E_{a} and N are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point E_{a} and point N
line m(H_{b}H_{c}) E_{a} N 

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



% NDG:  line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect% DET:  points E_{a} and M_{a} must be different
% Constructing a point M_{a} which is an image of the point E_{a} in the symmetry to point/line N
sim M_{a} N E_{a} 
cmark_b M_{a}


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

color 200 200 200
drawline a
color 0 0 0




% Constructing a point A such that E_{a}A/E_{a}H_{a}=0.7876223686239064
towards A E_{a} H_{a} 0.7876223686239064 
cmark_t A
color 200 200 200
drawsegment E_{a} H_{a} 
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



% Constructing a point O such that NO/NH=-1
towards O N H -1 
cmark_t O
color 200 200 200
drawsegment H O 
color 0 0 0


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

color 200 200 200
drawcircle k(O,C)
color 0 0 0



% NDG:  line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a 
cmark_b C
cmark_b B



drawsegment A B
drawsegment A C
drawsegment B C

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