Construction in GCLC language

dim 120 120

point M_{a} 65 40
point N 72.5 61.93

color 220 0 0
fontsize 11

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

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



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

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




% Generating number V[_G40503] with value 0.9341979771234339
number V[_G40503] 0.9341979771234339 


% Calculating value V[_G40524] using formula V[_G40503]*360
expression V[_G40524]  { V[_G40503]*360  } 


% Constructing a point E_{c} which is an image of the point V[_G40524] in a rotation around the point N for the angle M_{a}
rotate E_{c} N V[_G40524] M_{a} 
color 220 0 0
fontsize 11
cmark_r E_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{a} V[_G40524] 
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_{c}) and circle k(N,M_{a}) intersect% DET:  points M_{a} and E_{a} must be different
% Constructing a point E_{a} which is an image of the point M_{a} in the symmetry to point/line N
sim E_{a} N M_{a} 
cmark_r E_{a}


% 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}



% Constructing a free point A
point A 80 95

cmark_t A



% 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 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



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