From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR ?

13, 12

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13, 13

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12, 12

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12, 18

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Solution

The correct option is C 12, 12

Clearly tangent PQ and PR are perpendicular to radii OQ and OR respectively.

Hence both triangles POQ and PQR are right angled.
$∴ P Q = \sqrt{{O P}^{2} - {O Q}^{2}}$ = $\sqrt{13^{2} - 5^{2}}$
$P R$ = $\sqrt{{O P}^{2} - {O R}^{2}}$ = $\sqrt{13^{2} - 5^{2}}$
so, $P R = P Q = 12 c m$
option C will be the answer.

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Similar questions

Q. From a point which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, a pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR?

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From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. What are the lengths (in cm) of tangents PQ and PR ?

The correct option is C 12, 12Clearly tangent PQ and PR are perpendicular to radii OQ and OR respectively.Hence both triangles POQ and PQR are right angled.∴PQ=√OP2−OQ2 = √132−52PR= √OP2−OR2=√132−52so,PR=PQ=12cmoption C will be the answer.