Construction in GCLC language

dim 120 120

point M_{b} 95 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt M_{b}
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 M_{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 M_{b}
circle k(N,M_{a}) N M_{b} 

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




% Generating number V[_G54510] with value 0.4961465717906315
number V[_G54510] 0.4961465717906315 


% Calculating value V[_G54531] using formula V[_G54510]*360
expression V[_G54531]  { V[_G54510]*360  } 


% Constructing a point E_{a} which is an image of the point V[_G54531] in a rotation around the point N for the angle M_{b}
rotate E_{a} N V[_G54531] M_{b} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{b} V[_G54531] 
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}



% Constructing a free point A
point A 80 95

cmark_t A



% 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



% Constructing a line L_{\_G55014} which passes through point A and point M_{a}
line L_{\_G55014} A M_{a} 

color 200 200 200
drawline L_{\_G55014}
color 0 0 0


% Constructing a point P_{\_G55115} with coordinates (0,0)
point P_{\_G55115} 0 0 
cmark_r P_{\_G55115}

% Constructing a point P_{\_G55039} such that AP_{\_G55039}/AP_{\_G55115}=2
towards P_{\_G55039} A P_{\_G55115} 2 
cmark_r P_{\_G55039}
color 200 200 200
drawsegment A P_{\_G55039} 
color 0 0 0

% Constructing a point P_{\_G55084} such that AP_{\_G55084}/AP_{\_G55115}=3
towards P_{\_G55084} A P_{\_G55115} 3 
cmark_r P_{\_G55084}
color 200 200 200
drawsegment A P_{\_G55084} 
color 0 0 0

% Constructing a line L_{\_G55045} which passes through point M_{a} and point P_{\_G55084}
line L_{\_G55045} M_{a} P_{\_G55084} 

color 200 200 200
drawline L_{\_G55045}
color 0 0 0


% Constructing a line L_{\_G55008} which contains the point P_{\_G55039} and is parallel to the line L_{\_G55045}
parallel L_{\_G55008} P_{\_G55039} L_{\_G55045} 

color 200 200 200
drawline L_{\_G55008}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G55008} and line L_{\_G55014}
intersec G L_{\_G55008} L_{\_G55014} 
cmark_t G



% Constructing a point B such that M_{b}B/M_{b}G=3
towards B M_{b} G 3 
cmark_b B
color 200 200 200
drawsegment M_{b} B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

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