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Question
In the given figure, PA and PB are the tangent segemtns to a circle with centre O. Show that he points A, O, B and P are concyclic.
Solution
Here, OA = OB
And OA ⊥ AP,OA ⊥ BP (Since tangents drawn from an external point are perpendicular to the radius at the point of contact)
∴ ∠ OAP = 90° , ∠ OBP = 90°
∴ ∠OAP +∠ OBP = 90° + 90° = 180°
∴ ∠ AOB + ∠APB =180° (Since, ∠OAP +∠OBP +∠AOB +∠APB = 360° )
Sum of opposite angle of a quadrilateral is 180° .
Hence A, O, B and P are concyclic.
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