From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isA. 7 cmB. 12 cmC. 15 cmD. 24.5 cm

Given:

OQ = 25 cm

PQ = 24 cm

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆POQ is right-angled at OPQ.

Therefore,

By Pythagoras Theorem in ∆POQ,

OP2 + PQ2 =OQ2

OP2 = OQ2 – PQ 2

OP= √( OQ2 – PQ 2)

OP= √(252 – 242)

OP= √(625 – 576)

OP = 49 cm

OP = 7 cm

Hence, OP = 7 cm

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