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

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



% 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[_G114087] with value 0.49810228737738294
number V[_G114087] 0.49810228737738294 


% Calculating value V[_G114108] using formula V[_G114087]*360
expression V[_G114108]  { V[_G114087]*360  } 


% Constructing a point H_{c} which is an image of the point V[_G114108] in a rotation around the point N for the angle M_{c}
rotate H_{c} N V[_G114108] M_{c} 
color 220 0 0
fontsize 11
cmark_lt H_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{c} V[_G114108] 
color 0 0 0


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

color 200 200 200
drawline c
color 0 0 0



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


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

color 200 200 200
drawline h_{c}
color 0 0 0




% Constructing a point A such that H_{c}A/H_{c}M_{c}=0.49810228737738294
towards A H_{c} M_{c} 0.49810228737738294 
cmark_t A
color 200 200 200
drawsegment H_{c} M_{c} 
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


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

color 200 200 200
drawcircle k(M_{c},A)
color 0 0 0



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


% 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_{c} and h_{a} are not parallel% DET:  lines h_{c} and h_{a} are not the same
% Constructing a point H which belongs to line h_{c} and line h_{a}
intersec H h_{c} h_{a} 
cmark_rt H



% Constructing a line L_{\_G115008} which passes through point N and point H
line L_{\_G115008} N H 

color 200 200 200
drawline L_{\_G115008}
color 0 0 0


% Constructing a point P_{\_G115109} with coordinates (0,0)
point P_{\_G115109} 0 0 
cmark_r P_{\_G115109}

% Constructing a point P_{\_G115033} such that NP_{\_G115033}/NP_{\_G115109}=-1
towards P_{\_G115033} N P_{\_G115109} -1 
cmark_r P_{\_G115033}
color 200 200 200
drawsegment P_{\_G115109} P_{\_G115033} 
color 0 0 0

% Constructing a point P_{\_G115078} such that NP_{\_G115078}/NP_{\_G115109}=3
towards P_{\_G115078} N P_{\_G115109} 3 
cmark_r P_{\_G115078}
color 200 200 200
drawsegment N P_{\_G115078} 
color 0 0 0

% Constructing a line L_{\_G115039} which passes through point H and point P_{\_G115078}
line L_{\_G115039} H P_{\_G115078} 

color 200 200 200
drawline L_{\_G115039}
color 0 0 0


% Constructing a line L_{\_G115002} which contains the point P_{\_G115033} and is parallel to the line L_{\_G115039}
parallel L_{\_G115002} P_{\_G115033} L_{\_G115039} 

color 200 200 200
drawline L_{\_G115002}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G115002} and line L_{\_G115008}
intersec G L_{\_G115002} L_{\_G115008} 
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:  lines h_{c} and h_{a} are not parallel; circles k(N,M_{a}) and k(M_{c},A) intersect; points A and M_{c} are not the same; line m(H_{b}H_{a}) and circle k(N,M_{a}) intersect; points M_{c} and N are not the same
% Determination conditions:  lines h_{c} and h_{a} are not the same; points A and H_{a} are not the same; circles k(N,M_{a}) and k(M_{c},A) are not the same; points E_{c} and H_{c} are not the same; points M_{c} and E_{c} must be different; points H_{c} and M_{c} are not the same; points M_{c} and N are not the same