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.

By Pythagoras theorem,

OQ² = OP² + PQ²

25² = r² + 24²

r² = 25² - 24²

r² = 625 - 576

r² = 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.