HYACINTHOS 21959

[Antreas P. Hatzipolakis]:

> Let ABC be a triangle, P, P* two isogonala conjugate points.
>
> Denote:
>
> Ra = radical axis of (NPC_PBC), (NPC_P*BC)
>
> Rb = radical axis of (NPC_PCA), (NPC_P*CA)
>
> Rc = radical axis of (NPC_PAB), (NPC_P*AB)
>
> Which is the locus of P such that Ra,Rb,Rc are concurrent?
> The entire plane?
>
> Antreas

[Barry Wolk]:

This was already answered, and is the whole plane.
Another way of stating this result is:
 
The Poncelet points of the quads BCPP*, CAPP*, ABPP*
form a triangle which is perspective to the medial triangle.
--
Barry Wolk