Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point M_{a} 65 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b M_{a}
color 0 0 0
fontsize 10


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

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



% DET:  points E_{a} and M_{a} are not the same
% Constructing bisector m(E_{a}M_{a}) of the segment E_{a}M_{a}
med m(E_{a}M_{a}) E_{a} M_{a} 

color 200 200 200
drawline m(E_{a}M_{a})
color 0 0 0

color 200 200 200
drawsegment E_{a} M_{a} 
color 0 0 0


% NDG:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel% DET:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same
% Constructing a point N which belongs to line m(E_{a}M_{a}) and line m(H_{b}H_{c})
intersec N m(E_{a}M_{a}) m(H_{b}H_{c}) 
cmark_r N


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

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




% Generating number V[_G44703] with value 0.5735488458069573
number V[_G44703] 0.5735488458069573 


% Calculating value V[_G44724] using formula V[_G44703]*360
expression V[_G44724]  { V[_G44703]*360  } 


% Constructing a point M_{c} which is an image of the point V[_G44724] in a rotation around the point N for the angle E_{a}
rotate M_{c} N V[_G44724] E_{a} 
color 220 0 0
fontsize 11
cmark_lt M_{c}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N E_{a} V[_G44724] 
color 0 0 0



% 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_{\_G45027} which passes through point A and point M_{a}
line L_{\_G45027} A M_{a} 

color 200 200 200
drawline L_{\_G45027}
color 0 0 0


% Constructing a point P_{\_G45128} with coordinates (0,0)
point P_{\_G45128} 0 0 
cmark_r P_{\_G45128}

% Constructing a point P_{\_G45052} such that AP_{\_G45052}/AP_{\_G45128}=2
towards P_{\_G45052} A P_{\_G45128} 2 
cmark_r P_{\_G45052}
color 200 200 200
drawsegment A P_{\_G45052} 
color 0 0 0

% Constructing a point P_{\_G45097} such that AP_{\_G45097}/AP_{\_G45128}=3
towards P_{\_G45097} A P_{\_G45128} 3 
cmark_r P_{\_G45097}
color 200 200 200
drawsegment A P_{\_G45097} 
color 0 0 0

% Constructing a line L_{\_G45058} which passes through point M_{a} and point P_{\_G45097}
line L_{\_G45058} M_{a} P_{\_G45097} 

color 200 200 200
drawline L_{\_G45058}
color 0 0 0


% Constructing a line L_{\_G45021} which contains the point P_{\_G45052} and is parallel to the line L_{\_G45058}
parallel L_{\_G45021} P_{\_G45052} L_{\_G45058} 

color 200 200 200
drawline L_{\_G45021}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G45021} and line L_{\_G45027}
intersec G L_{\_G45021} L_{\_G45027} 
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:  points E_{a} and N are not the same; lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not parallel
% Determination conditions:  lines m(E_{a}M_{a}) and m(H_{b}H_{c}) are not the same; points E_{a} and M_{a} are not the same; points E_{a} and M_{a} are not the same