# 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

**Solution:**

Let's draw a figure as per the given dimensions.

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

Therefore, OPQ is a right-angled triangle.

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

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

r^{2} = 25^{2} - 24^{2}

r^{2} = 625 - 576

r^{2} = 49

r = ± 7

Radius cannot be a negative value, Hence, r = 7 cm.

Thus, option (A) 7 cm is the correct answer.

**Video 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 (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm

### Maths NCERT Solutions Class 10 - Chapter 10 Exercise 10.2 Question 1:

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

If from a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the center is 25 cm, then the radius of the circle is 7cm