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

Let O be the centre of two concentric circles C₁ and C₂, whose radii are r₁ = 4 cm and r₂ = 5 cm.

Now, we draw a chord AC of circle C₂, which touches the circle C₁ at B.

Also, join OB, which is perpendicular to AC.

[∵ Tangent at any point of circle is perpendicular to radius through the point of contact]

Now, in right angled ∆OBC,

By using Pythagoras theorem,

OC² = BC² + BO²     ...[∵ (Hypotenuse)² = (Base)² + (Perpendicular)²]

⇒ 5² = BC² + 4²

⇒ BC² = 25 – 16 = 9

⇒ BC = 3 cm

∴ Length of chord AC = 2BC

= 2 × 3

= 6 cm