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Question

# State the following statement is True or FalseThe length of two tangents drawn from an external point to a circle are unequal.

A
True
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B
False
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Solution

## The correct option is B FalseThe lengths of tangents drawn from an external point to a circle are equal. Proof: We are given a circle with centre O, a point P lying outside the circle and two tangents PQ, PR on the circle from P (see Fig.) We are required to prove that PQ=PR. For this, we join OP,OQ and OR. Then ∠OQP and ∠ORP are right angles, because these are angles between the radii and tangents. Now in right triangles OQP and ORP, OQ=OR (Radii of the same circle) OP=OP (Common) Therefore, ΔOQP≅ΔORP (RHS) This gives PQ=PR (CPCT)This implies that the given statement is false because it states that "The lengths of tangents drawn from an external point to a circle are unequal."

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