NPC center of the Cevian triangle of I

Let ABC be a triangle, A'B'C' the cevian triangle of I, I' the isogonal conjugate of I wrt A'B'C' and N' the NPC center of A'B'C'.

Conjecture 1:

The points I, N',I' are collinear.

Conjecture 2:

Let A"B"C" be the pedal triangle of I' wrt A'B'C'.

I' is the NPC center A"B"C".(Randy Hutson)

The line II' is the Euler line of A"B"C"

Antreas P. Hatzipolakis, 15 May 2013

Anopolis #255 (Re: NPC center of the cevian triangle of I)