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In the given figure, PA and PB are the tangent segments to a circle with centre O. Show that the points A, O, B and P are concyclic.

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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.

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