Trigonometry/Reflections in a triangle

Take any triangle ABC and any point P.

Let X be the reflection of P in BC (or BC extended), Y be the reflection of P in AC (or AC extended) and Z be the reflection of P in AB (or AB extended).

Then the four circles XYC, YZA, ZXB and the circumcircle of ABC all paas through the same point, the reflection of P in ABC.