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_{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[_G125649] with value 0.5419591545920769
number V[_G125649] 0.5419591545920769 


% Calculating value V[_G125670] using formula V[_G125649]*360
expression V[_G125670]  { V[_G125649]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G125670] in a rotation around the point N for the angle M_{c}
rotate H_{a} N V[_G125670] M_{c} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N M_{c} V[_G125670] 
color 0 0 0


% NDG:  points H_{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 H_{a}
circle k(M_{c},A) M_{c} H_{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; points H_{a} and H_{b} must be different
% Constructing a line L_{\_G126085} which passes through point N and point M_{c}
line L_{\_G126085} N M_{c} 

color 200 200 200
drawline L_{\_G126085}
color 0 0 0


% Constructing a point H_{b} which is an image of the point H_{a} in the symmetry to point/line L_{\_G126085}
sim H_{b} L_{\_G126085} H_{a} 
cmark_rt H_{b}



% Generating number V[_G126187] with value 0.5419591545920769
number V[_G126187] 0.5419591545920769 


% Calculating value V[_G126208] using formula V[_G126187]*360
expression V[_G126208]  { V[_G126187]*360  } 


% Constructing a point A which is an image of the point V[_G126208] in a rotation around the point M_{c} for the angle H_{a}
rotate A M_{c} V[_G126208] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{a} V[_G126208] 
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


% 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



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

color 200 200 200
drawline h_{b}
color 0 0 0



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



% Constructing a line L_{\_G126620} which passes through point N and point H
line L_{\_G126620} N H 

color 200 200 200
drawline L_{\_G126620}
color 0 0 0


% Constructing a point P_{\_G126721} with coordinates (0,0)
point P_{\_G126721} 0 0 
cmark_r P_{\_G126721}

% Constructing a point P_{\_G126645} such that NP_{\_G126645}/NP_{\_G126721}=-1
towards P_{\_G126645} N P_{\_G126721} -1 
cmark_r P_{\_G126645}
color 200 200 200
drawsegment P_{\_G126721} P_{\_G126645} 
color 0 0 0

% Constructing a point P_{\_G126690} such that NP_{\_G126690}/NP_{\_G126721}=3
towards P_{\_G126690} N P_{\_G126721} 3 
cmark_r P_{\_G126690}
color 200 200 200
drawsegment N P_{\_G126690} 
color 0 0 0

% Constructing a line L_{\_G126651} which passes through point H and point P_{\_G126690}
line L_{\_G126651} H P_{\_G126690} 

color 200 200 200
drawline L_{\_G126651}
color 0 0 0


% Constructing a line L_{\_G126614} which contains the point P_{\_G126645} and is parallel to the line L_{\_G126651}
parallel L_{\_G126614} P_{\_G126645} L_{\_G126651} 

color 200 200 200
drawline L_{\_G126614}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G126614} and line L_{\_G126620}
intersec G L_{\_G126614} L_{\_G126620} 
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_{a} and h_{b} are not parallel; circles k(N,M_{a}) and k(M_{c},A) intersect; points H_{a} and M_{c} are not the same; points M_{c} and N are not the same
% Determination conditions:  lines h_{a} and h_{b} are not the same; points H_{b} and B 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 H_{a} and H_{b} must be different