REFLECTIONS - COLLINEARITY

Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P.

Denote:

A* = BC /\ (Reflection of B'C' in AA')

B* = CA /\ (Reflection of C'A' in BB')

C* = AB /\ (Reflection of A'B' in CC')

Which is the locus of P such that the A*,B*,C* are collinear?

The incenter I is on the locus

Antreas P; Hatzipolakis, 13 March 2013