Construction in GCLC language

dim 120 120

point H_{c} 68.91 84.83
point N 72.5 61.93

color 220 0 0
fontsize 11

cmark_lt H_{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 H_{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 H_{c}
circle k(N,M_{a}) N H_{c} 

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




% Generating number V[_G53281] with value 0.7324242298139407
number V[_G53281] 0.7324242298139407 


% Calculating value V[_G53302] using formula V[_G53281]*360
expression V[_G53302]  { V[_G53281]*360  } 


% Constructing a point H_{a} which is an image of the point V[_G53302] in a rotation around the point N for the angle H_{c}
rotate H_{a} N V[_G53302] H_{c} 
color 220 0 0
fontsize 11
cmark_b H_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p N H_{c} V[_G53302] 
color 0 0 0


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

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

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


% NDG:  line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect
% Constructing points M_{b} and E_{b} which are in intersection of k(N,M_{a}) and m(H_{a}H_{c})
intersec2 M_{b} E_{b} k(N,M_{a}) m(H_{a}H_{c}) 
cmark_rt M_{b}
cmark_r E_{b}



% Generating number V[_G53737] with value 0.7324242298139407
number V[_G53737] 0.7324242298139407 


% Calculating value V[_G53758] using formula V[_G53737]*360
expression V[_G53758]  { V[_G53737]*360  } 


% Constructing a point A which is an image of the point V[_G53758] in a rotation around the point M_{b} for the angle H_{a}
rotate A M_{b} V[_G53758] H_{a} 
cmark_t A
color 200 200 200
drawarc_p M_{b} H_{a} V[_G53758] 
color 0 0 0



% Constructing a point C such that AC/AM_{b}=2
towards C A M_{b} 2 
cmark_b C
color 200 200 200
drawsegment A C 
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_{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_{a} and h_{c} are not parallel% DET:  lines h_{a} and h_{c} are not the same
% Constructing a point H which belongs to line h_{a} and line h_{c}
intersec H h_{a} h_{c} 
cmark_rt H



% Constructing a line L_{\_G54169} which passes through point N and point H
line L_{\_G54169} N H 

color 200 200 200
drawline L_{\_G54169}
color 0 0 0


% Constructing a point P_{\_G54270} with coordinates (0,0)
point P_{\_G54270} 0 0 
cmark_r P_{\_G54270}

% Constructing a point P_{\_G54194} such that NP_{\_G54194}/NP_{\_G54270}=-1
towards P_{\_G54194} N P_{\_G54270} -1 
cmark_r P_{\_G54194}
color 200 200 200
drawsegment P_{\_G54270} P_{\_G54194} 
color 0 0 0

% Constructing a point P_{\_G54239} such that NP_{\_G54239}/NP_{\_G54270}=3
towards P_{\_G54239} N P_{\_G54270} 3 
cmark_r P_{\_G54239}
color 200 200 200
drawsegment N P_{\_G54239} 
color 0 0 0

% Constructing a line L_{\_G54200} which passes through point H and point P_{\_G54239}
line L_{\_G54200} H P_{\_G54239} 

color 200 200 200
drawline L_{\_G54200}
color 0 0 0


% Constructing a line L_{\_G54163} which contains the point P_{\_G54194} and is parallel to the line L_{\_G54200}
parallel L_{\_G54163} P_{\_G54194} L_{\_G54200} 

color 200 200 200
drawline L_{\_G54163}
color 0 0 0


% Constructing a point G which belongs to line L_{\_G54163} and line L_{\_G54169}
intersec G L_{\_G54163} L_{\_G54169} 
cmark_t G



% Constructing a point B such that M_{b}B/M_{b}G=3
towards B M_{b} G 3 
cmark_b B
color 200 200 200
drawsegment M_{b} B 
color 0 0 0



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines h_{a} and h_{c} are not parallel; line m(H_{a}H_{c}) and circle k(N,M_{a}) intersect; points H_{c} and N are not the same
% Determination conditions:  lines h_{a} and h_{c} are not the same; points H_{c} and C are not the same; points A and H_{a} are not the same; points H_{a} and H_{c} are not the same