Pre RMO

Geometry Level 5

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.

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