HYACINTHOS 29640

[Antreas P. Hatzipolakis]:

Let ABC be a triangle.

Denite:

Na, Nb, Nc = the NPC centers of NBC, NCA, NAB, resp.

A' = BC /\ NbNc
B' = CA /\ NcNa
C' = AB /\ NaNb

A', B',C' are collinear.

Which line is A'B'C' ? (trilinear polar of which point?)


[Peter Moses]:


Hi Antreas,

5*a^12 - 20*a^10*b^2 + 31*a^8*b^4 - 24*a^6*b^6 + 11*a^4*b^8 - 4*a^2*b^10 + b^12 - 20*a^10*c^2 + 32*a^8*b^2*c^2 - 4*a^6*b^4*c^2 - 16*a^4*b^6*c^2 + 16*a^2*b^8*c^2 - 8*b^10*c^2 + 31*a^8*c^4 - 4*a^6*b^2*c^4 + 7*a^4*b^4*c^4 - 12*a^2*b^6*c^4 + 23*b^8*c^4 - 24*a^6*c^6 - 16*a^4*b^2*c^6 - 12*a^2*b^4*c^6 - 32*b^6*c^6 + 11*a^4*c^8 + 16*a^2*b^2*c^8 + 23*b^4*c^8 - 4*a^2*c^10 - 8*b^2*c^10 + c^12  :  :

= lies on this line: {2, 6}


Best regards,
Peter Moses.