Pre RMO

Geometry Level 4

In the figure below,

the smaller circle touches the bigger circle at $P$ . The centre of the bigger circle is $O$ . Let $XY$ be the diameter of the bigger circle which is also tangent to smaller circle. Let $PY$ intersect the smaller circle at $Z$ . If $YZ = 2PZ$ , find the magnitue of angle $PYX$ in degrees.