Construction in GCLC language

dim 120 120

point H_{b} 89.36 77.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_rt H_{b}
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 H_{b} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point H_{b}
circle k(N,M_{a}) N H_{b} 

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




% Generating number V[_G54865] with value 0.5869047092822781
number V[_G54865] 0.5869047092822781 


% Calculating value V[_G54886] using formula V[_G54865]*360
expression V[_G54886]  { V[_G54865]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G54886] in a rotation around the point N for the angle H_{b}
rotate H_{a} N V[_G54886] H_{b} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{b} V[_G54886] 
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:  line m(H_{a}H_{b}) and circle k(N,M_{a}) intersect
% Constructing points M_{c} and E_{c} which are in intersection of k(N,M_{a}) and m(H_{a}H_{b})
intersec2 M_{c} E_{c} k(N,M_{a}) m(H_{a}H_{b}) 
cmark_lt M_{c}
cmark_r E_{c}



% Generating number V[_G55321] with value 0.5869047092822781
number V[_G55321] 0.5869047092822781 


% Calculating value V[_G55342] using formula V[_G55321]*360
expression V[_G55342]  { V[_G55321]*360  } 


% Constructing a point A which is an image of the point V[_G55342] in a rotation around the point M_{c} for the angle H_{a}
rotate A M_{c} V[_G55342] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{c} H_{a} V[_G55342] 
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_{\_G55753} which passes through point N and point H
line L_{\_G55753} N H 

color 200 200 200
drawline L_{\_G55753}
color 0 0 0


% Constructing a point P_{\_G55854} with coordinates (0,0)
point P_{\_G55854} 0 0 
cmark_r P_{\_G55854}

% Constructing a point P_{\_G55778} such that NP_{\_G55778}/NP_{\_G55854}=-1
towards P_{\_G55778} N P_{\_G55854} -1 
cmark_r P_{\_G55778}
color 200 200 200
drawsegment P_{\_G55854} P_{\_G55778} 
color 0 0 0

% Constructing a point P_{\_G55823} such that NP_{\_G55823}/NP_{\_G55854}=3
towards P_{\_G55823} N P_{\_G55854} 3 
cmark_r P_{\_G55823}
color 200 200 200
drawsegment N P_{\_G55823} 
color 0 0 0

% Constructing a line L_{\_G55784} which passes through point H and point P_{\_G55823}
line L_{\_G55784} H P_{\_G55823} 

color 200 200 200
drawline L_{\_G55784}
color 0 0 0


% Constructing a line L_{\_G55747} which contains the point P_{\_G55778} and is parallel to the line L_{\_G55784}
parallel L_{\_G55747} P_{\_G55778} L_{\_G55784} 

color 200 200 200
drawline L_{\_G55747}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G55747} and line L_{\_G55753}
intersec G L_{\_G55747} L_{\_G55753} 
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; line m(H_{a}H_{b}) and circle k(N,M_{a}) intersect; points H_{b} 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; points H_{a} and H_{b} are not the same