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Radius and Tangent to a Circle Are Perpendicular

From a point ...

Question

From a point P outside the circle, with centre O, tangents PA and PB are drawn.Then ∠AOP is equal to

∠APO

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∠PAO

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∠BOP

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∠APB

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Solution

The correct option is C ∠BOP

In △AOP and △BOP,

AP = BP (Tangents from P to the circle)

OP = OP (Common)

OA = OB (Radii of the same circle)

By Side-Side-Side congruence , AOP is congruent to BOP.

As the corresponding parts of congruent triangles are equal,

∠AOP = ∠BOP

Therefore, option c is correct.

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Similar questions

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Then, select the statements that are true.

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that :

(i) $∠ A O P = ∠ B O P$ ,

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