Find The Angle

Geometry Level 4

In acute ABC\triangle ABC with AB<AC,AB<AC, the tangent to the circumcircle passing through CC meets line ABAB at S.S. Let PP be a point in the interior of ABC\triangle ABC such that SC=SP.SC= SP. Lines BP,APBP, AP meet the circumcircle at points X,ZX, Z respectively. Suppose that PSZ=60.\angle PSZ= 60^{\circ}. Find SZX\angle SZX in degrees.

Details and assumptions
- The diagram shown is not accurate, so don't rely on it for non-trivial observations.
- This problem is inspired by IMOSL 2010 G2.


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