HYACINTHOS 25737

[Tran Quang Hung]:

 

Let ABC be a triangle with two Fermat point F1,F2.

 

M is midpoint of F1F2 then M lies on NPC of ABC.

 

Ma,Mb,Mc are midpoints of BC,CA,AB, reps.

 

NPC of triangles AF1F2,BF1F2,CF1F2 intersects NPC of ABC at A',B',C' other than M.

 

G is centroid of triangle ABC.

 

Then the lines MaA',MbB',McC' and MG are concurent.

 

Which is this point ?

 

 

[César Lozada]:

 

 

Z = (3*SA-SW)*(6*SA^2-(9*R^2+2*SW) *SA+6*S^2-2*SW^2+3*R^2*SW) : :  (barycentrics)

= On lines: {2,99}, {5,5099}, {3580,10413}

= [ 2.883964049976410, 0.72437017953226, 1.808117103780623 ]

 

César Lozada