Construction in GCLC language

dim 120 120

point M_{c} 50 67.5
point H_{b} 89.36 77.83

color 220 0 0
fontsize 11

cmark_lt M_{c}
cmark_rt H_{b}
color 0 0 0
fontsize 10


% point H_{a} is given by the problem setting, but it has to belong to the circle k(M_{c},A) which is constructible from the others objects given 
% NDG:  points H_{b} 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_{b}
circle k(M_{c},A) M_{c} H_{b} 

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




% Generating number V[_G41022] with value 0.008926615346747473
number V[_G41022] 0.008926615346747473 


% Calculating value V[_G41043] using formula V[_G41022]*360
expression V[_G41043]  { V[_G41022]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G41043] in a rotation around the point M_{c} for the angle H_{b}
rotate H_{a} M_{c} V[_G41043] H_{b} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p M_{c} H_{b} V[_G41043] 
color 0 0 0


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

color 200 200 200
drawline m(H_{a}M_{c})
color 0 0 0

color 200 200 200
drawsegment H_{a} M_{c} 
color 0 0 0


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

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

color 200 200 200
drawsegment H_{a} H_{b} 
color 0 0 0


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



% Generating number V[_G41682] with value 0.008926615346747473
number V[_G41682] 0.008926615346747473 


% Calculating value V[_G41703] using formula V[_G41682]*360
expression V[_G41703]  { V[_G41682]*360  } 


% Constructing a point A which is an image of the point V[_G41703] in a rotation around the point M_{c} for the angle H_{a}
rotate A M_{c} V[_G41703] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{a} V[_G41703] 
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_{\_G42114} which passes through point N and point H
line L_{\_G42114} N H 

color 200 200 200
drawline L_{\_G42114}
color 0 0 0


% Constructing a point P_{\_G42215} with coordinates (0,0)
point P_{\_G42215} 0 0 
cmark_r P_{\_G42215}

% Constructing a point P_{\_G42139} such that NP_{\_G42139}/NP_{\_G42215}=-1
towards P_{\_G42139} N P_{\_G42215} -1 
cmark_r P_{\_G42139}
color 200 200 200
drawsegment P_{\_G42215} P_{\_G42139} 
color 0 0 0

% Constructing a point P_{\_G42184} such that NP_{\_G42184}/NP_{\_G42215}=3
towards P_{\_G42184} N P_{\_G42215} 3 
cmark_r P_{\_G42184}
color 200 200 200
drawsegment N P_{\_G42184} 
color 0 0 0

% Constructing a line L_{\_G42145} which passes through point H and point P_{\_G42184}
line L_{\_G42145} H P_{\_G42184} 

color 200 200 200
drawline L_{\_G42145}
color 0 0 0


% Constructing a line L_{\_G42108} which contains the point P_{\_G42139} and is parallel to the line L_{\_G42145}
parallel L_{\_G42108} P_{\_G42139} L_{\_G42145} 

color 200 200 200
drawline L_{\_G42108}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G42108} and line L_{\_G42114}
intersec G L_{\_G42108} L_{\_G42114} 
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; lines m(H_{a}H_{b}) and m(H_{a}M_{c}) are not parallel; points H_{b} and M_{c} 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; lines m(H_{a}H_{b}) and m(H_{a}M_{c}) are not the same; points H_{a} and H_{b} are not the same; points H_{a} and M_{c} are not the same