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in Mathematics by (33.1k points)

Prove that the lengths of two tangents drawn from an external point to a circle are equal.

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Given two tangents AP and AQ are drawn from a point A to a circle with center O. 

To prove: AP = AQ 

Join OP, OQ and OA.

AP is tangent at P and OP is the radius

OP ⊥ AP (Since tangents drawn from an external point are perpendicular to the radius at the point of contact)

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