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Question

# In the given figure, the pair of tangents AP and AQ, drawn from an external point A to a circle with center O, are perpendicular to each other and length of each tangent is 4 cm, then the radius of the circle is

A
10 cm
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B
7.5 cm
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C
2.5 cm
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D
4 cm
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Solution

## The correct option is D 4 cmJoin OA.Triangles OPA and OQA are congruent.⇒∠PAO=∠QAO=45oTangent and radius are perpendicular at the point of contact.∠OPA=90o⇒∠OAP=∠AOP=45o⇒OP=AP=4cmSo the radius of the circle is 4 cm.So option D is the right answer.

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