#### Question

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

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#### Solution

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 = 7

Therefore, the radius of the circle is 7 cm.

Hence, alternative (A) is correct.

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#### Reference Material

Solution for question: 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 concept: Number of Tangents from a Point on a Circle. For the course CBSE