Parallel Lines : GENERALIZATION 1

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

Denote (for I, J : the incenters of ABC, A'B'C', resp.):
L1,L2,L3 := the reflections of AI, BI, CI in L, resp.
M1,M2,M3 := the reflections of the bisectors A'J, B'J, C'J of the triangle A'B'C' in L1, L2, L3, resp

Which is the locus of P such that the lines M1,M2,M3 are concurrent?

APH, 12 December 2011