Question

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

BC is tangent to a small circle.

BC is a chord of a large circle.

OA = 4 cm

OB = 5 cm

OA ⊥ BC   ...[∵ The tangent to a circle is perpendicular to the radius through the point of contact.]

∠ OAB = 90°

In Δ OAB, by using Pythagoras theorem,

OB² = OA² + AB²     ...[∵ (Hypotenuse)² = (Base)² + (Perpendicular)²]

⇒ (5)² = (4)² + AB²

⇒ 25 = 16 + AB²

⇒ 25 − 16 = AB²

⇒ AB² = 9

⇒ AB = 3 cm

∴ Length of chord BC = 2AB

= 2 × 3

= 6 cm

Therefore, the length of the chord of the larger circle which touches the smaller circle is 6 cm.