Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point N 72.5 61.93

color 220 0 0
fontsize 11

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

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




% Generating number V[_G61975] with value 0.31133410452689547
number V[_G61975] 0.31133410452689547 


% Calculating value V[_G61996] using formula V[_G61975]*360
expression V[_G61996]  { V[_G61975]*360  } 


% Constructing a point E_{a} which is an image of the point V[_G61996] in a rotation around the point N for the angle M_{c}
rotate E_{a} N V[_G61996] M_{c} 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{c} V[_G61996] 
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 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 line L_{\_G62479} which passes through point A and point M_{a}
line L_{\_G62479} A M_{a} 

color 200 200 200
drawline L_{\_G62479}
color 0 0 0


% Constructing a point P_{\_G62580} with coordinates (0,0)
point P_{\_G62580} 0 0 
cmark_r P_{\_G62580}

% Constructing a point P_{\_G62504} such that AP_{\_G62504}/AP_{\_G62580}=2
towards P_{\_G62504} A P_{\_G62580} 2 
cmark_r P_{\_G62504}
color 200 200 200
drawsegment A P_{\_G62504} 
color 0 0 0

% Constructing a point P_{\_G62549} such that AP_{\_G62549}/AP_{\_G62580}=3
towards P_{\_G62549} A P_{\_G62580} 3 
cmark_r P_{\_G62549}
color 200 200 200
drawsegment A P_{\_G62549} 
color 0 0 0

% Constructing a line L_{\_G62510} which passes through point M_{a} and point P_{\_G62549}
line L_{\_G62510} M_{a} P_{\_G62549} 

color 200 200 200
drawline L_{\_G62510}
color 0 0 0


% Constructing a line L_{\_G62473} which contains the point P_{\_G62504} and is parallel to the line L_{\_G62510}
parallel L_{\_G62473} P_{\_G62504} L_{\_G62510} 

color 200 200 200
drawline L_{\_G62473}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G62473} and line L_{\_G62479}
intersec G L_{\_G62473} L_{\_G62479} 
cmark_t G



% Constructing a point C such that M_{c}C/M_{c}G=3
towards C M_{c} G 3 
cmark_b C
color 200 200 200
drawsegment M_{c} C 
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_{c} 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