PA and PB are tangents to a circle with center O (given)
To show: Points A, O, B and P are concyclic.
Since OB ⏊ PB and OA ⏊ AP
∠OBP = ∠OAP = 90°
∠OBP + ∠OAP = 90 + 90 = 180°
[Sum of opposite angles in a quadrilateral is 180°]
AOBP is a cyclic quadrilateral, thus A, O, B and P are concyclic.
Hence proved.