A NPC CENTER ON THE EULER LINE

Let ABC be a triangle and N1,N2,N3 the NPC centers of OBC, OCA, OAB, resp.

The NPC center of N1N2N3 lies on the Euler line of ABC.

Antreas P. Hatzipolakis, 30 May 2013

***************************************************** The barycentric coordinates of the NPC center of N1N2N3 are:

( 2a^10 - 5a^8(b^2+c^2) + 2a^6(b^4+5b^2c^2+c^4) + a^4(4b^6-5b^4c^2-5b^2c^4+4c^6) - a^2(b^2-c^2)^2(4b^4+5b^2c^2+4c^4) + (b^2-c^2)^4(b^2+c^2) : ... : ...)

with (6-9-13)-search number: 4.7800096839999025703058

Angel Montesdeoca, Anopolis #331