Pre RMO

Geometry Level 4

In the figure below,

the smaller circle touches the bigger circle at PP. The centre of the bigger circle is OO. Let XYXY be the diameter of the bigger circle which is also tangent to smaller circle. Let PYPY intersect the smaller circle at ZZ. If YZ=2PZYZ = 2PZ, find the magnitue of angle PYXPYX in degrees.

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