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# 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 question.

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

**☛ Check: **NCERT Solutions Class 10 Maths Chapter 10

**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

**Summary:**

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.

**☛ Related Questions:**

- In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to(A) 60°(B) 70°(C) 80°(D) 90°
- If tangents PA and PB from a point P to a circle with center O are inclined to each other at angle of 80°, then ∠POA is equal to(A) 50°(B) 60°(C) 70°(D) 80°
- Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
- Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

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