A geometry problem by Mehul Chaturvedi

Geometry Level 3

A circle with centre \(O \) is touching two intersecting lines \(AX\) and \(BY\). The two points of contact \(A\) and \(B\) subtend an angle of 65 degreess at any point C on the circumference of the circle. If \(P \) is the point of the intersection of the two lines, then find the measure of angle \(APO \) given that straight lines \(AP\) and \(PB\) are tangents.

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