Concurrent Circles

Let ABC be a triangle.
Let P be a point on the plane of ABC.
Let a, b, c, are the sides opposite vertices A, B, C.
Let P_a be the reflection of P around the perpendicular
bisector of a. Define P_b, P_c cyclically.

Then, circles (AP_bP_c), (BP_aP_c), (CP_aP_b) are concurrent at
the circumcircle of ABC.

Proof