Q. 24.6( 14 Votes )

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 is
A. 7 cm

B. 12 cm

C. 15 cm

D. 24.5 cm

Answer :

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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