Construction in GCLC language

dim 120 120

point M_{a} 65 40
point H_{c} 68.91 84.83

color 220 0 0
fontsize 11

cmark_b M_{a}
cmark_lt H_{c}
color 0 0 0
fontsize 10


% point H_{b} is given by the problem setting, but it has to belong to the circle k(M_{a},B) which is constructible from the others objects given 
% NDG:  points H_{c} and M_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point H_{c}
circle k(M_{a},B) M_{a} H_{c} 

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




% Generating number V[_G62002] with value 0.6025613020398952
number V[_G62002] 0.6025613020398952 


% Calculating value V[_G62023] using formula V[_G62002]*360
expression V[_G62023]  { V[_G62002]*360  } 


% Constructing a point H_{b} which is an image of the point V[_G62023] in a rotation around the point M_{a} for the angle H_{c}
rotate H_{b} M_{a} V[_G62023] H_{c} 
color 220 0 0
fontsize 11
cmark_rt H_{b}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p M_{a} H_{c} V[_G62023] 
color 0 0 0


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

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

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


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

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

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


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



% Generating number V[_G62662] with value 0.6025613020398952
number V[_G62662] 0.6025613020398952 


% Calculating value V[_G62683] using formula V[_G62662]*360
expression V[_G62683]  { V[_G62662]*360  } 


% Constructing a point B which is an image of the point V[_G62683] in a rotation around the point M_{a} for the angle H_{b}
rotate B M_{a} V[_G62683] H_{b} 
cmark_b B
color 200 200 200
drawarc_p M_{a} H_{b} V[_G62683] 
color 0 0 0



% Constructing a point C such that BC/BM_{a}=2
towards C B M_{a} 2 
cmark_b C
color 200 200 200
drawsegment B C 
color 0 0 0


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

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



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

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



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



% Constructing a line L_{\_G63094} which passes through point N and point H
line L_{\_G63094} N H 

color 200 200 200
drawline L_{\_G63094}
color 0 0 0


% Constructing a point P_{\_G63195} with coordinates (0,0)
point P_{\_G63195} 0 0 
cmark_r P_{\_G63195}

% Constructing a point P_{\_G63119} such that NP_{\_G63119}/NP_{\_G63195}=-1
towards P_{\_G63119} N P_{\_G63195} -1 
cmark_r P_{\_G63119}
color 200 200 200
drawsegment P_{\_G63195} P_{\_G63119} 
color 0 0 0

% Constructing a point P_{\_G63164} such that NP_{\_G63164}/NP_{\_G63195}=3
towards P_{\_G63164} N P_{\_G63195} 3 
cmark_r P_{\_G63164}
color 200 200 200
drawsegment N P_{\_G63164} 
color 0 0 0

% Constructing a line L_{\_G63125} which passes through point H and point P_{\_G63164}
line L_{\_G63125} H P_{\_G63164} 

color 200 200 200
drawline L_{\_G63125}
color 0 0 0


% Constructing a line L_{\_G63088} which contains the point P_{\_G63119} and is parallel to the line L_{\_G63125}
parallel L_{\_G63088} P_{\_G63119} L_{\_G63125} 

color 200 200 200
drawline L_{\_G63088}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G63088} and line L_{\_G63094}
intersec G L_{\_G63088} L_{\_G63094} 
cmark_t G



% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3 
cmark_t A
color 200 200 200
drawsegment M_{a} A 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{b} and h_{c} are not parallel; lines m(H_{b}H_{c}) and m(H_{b}M_{a}) are not parallel; points H_{c} and M_{a} are not the same
% Determination conditions:  lines h_{b} and h_{c} are not the same; points H_{c} and C are not the same; points B and H_{b} are not the same; lines m(H_{b}H_{c}) and m(H_{b}M_{a}) are not the same; points H_{b} and H_{c} are not the same; points H_{b} and M_{a} are not the same