#### 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

7 cm

12 cm

15 cm

24.5 cm

#### 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 7 cm is correct.

Is there an error in this question or solution?

Solution 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.