SIX CONCYCLIC CIRCUMCENTERS

Let ABC be a triangle, P a point, A'B'C' the cevian triangle of P wrt ABC and A"B"C" the cevian triangle of P wrt A'B'C' (ie A" = AA' /\ B'C' etc).

Denote:

A* = BC" /\ CB"

B* = CA" /\ AC"

C* = AB" /\ BA"

For which points P the circumcenters of the six triangles:

PA*B", PA*C", PB*C",PB*A", PC*A", PC*B" are concyclic?

Antreas P. Hatzipolakis, 26 April 2013