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

OP^{2} + PQ^{2} = OQ^{2}

OP^{2} + 24^{2} = 25^{2}

OP^{2} = 625 - 576

OP^{2} = 49

OP =

Therefore, the radius of the circle is 7 cm.

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