Measure of a Bisecting Angle

Geometry Level 3

Circle \(\Gamma\) with center \(O\) is tangential to \(PA\) at \(A\). Line \(PO\) extended intersects \(\Gamma\) at \(B\) (i.e. \(PO < PB\)). \(C\) is a point on \(AB\) such that \(PC\) bisects \( \angle APB\). What is the measure (in degrees) of \( \angle PCA\)?

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