NCERT Solutions for Class 10 Maths Chapter 10

Important NCERT Questions

Circles

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 10.2

Page No:214

Questions No:7

# Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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Let O be the centre of two concentric circles with radius 5 cm (OP) and 3 cm (OA). PQ is chord of larger circle which is a tangent to inner circle.

We know that the radius is perpendicular to tangent. Therefore, in ΔPQO, OA ⊥PQ.

In ΔAPO, by Pythagoras theorem,

OA² + AP² = OP²

⇒ 3² + AP² = 5²

⇒ 9 + AP² = 25 ⇒ AP² = 16 ⇒ AP = 4

In ΔOPQ, OA ⊥ PQ

AP = AQ [Perpendicular from the centre bisects the chord]

So, PQ = 2AP = 2 × 4 = 8

Hence, the length of chord of larger circle is 8 cm.