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

1. 7 cm

2. 12 cm

3. 15 cm

4. 24.5 cm

Let P be the point of contact of tangent with the circle and O be the center of the circle.

We know that,

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

So,

OP ⊥ PQ

In △OPQ,

By pythagoras theorem,

⇒ OQ² = OP² + PQ²

⇒ 25² = OP² + 24²

⇒ 625 = OP² + 576

⇒ OP² = 625 - 576

⇒ OP² = 49

⇒ OP = $\sqrt{49}$ = 7 cm.

Hence, Option 1 is the correct option.