Q. 14.5( 248 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 :

(A)


Let O be the centre of the circle.


Given that,


OQ = 25cm and PQ = 24 cm


As the radius is perpendicular to the tangent at the point of contact,


Therefore, OP PQ


Applying Pythagoras theorem in ΔOPQ, we obtain


OP2 + PQ2 = OQ2


OP2 + 242 = 252


OP2 = 625 - 576


OP2 = 49


OP =


Therefore, the radius of the circle is 7 cm.


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