Question

Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle (in cm) is

• A. 4
• B. 6
• C. 8
• D. 10

Hint:

If a chord of a larger circle touches a concentric smaller circle, then the distance of the chord from the center equals the radius of the smaller circle.

Answer 1

The Correct Option is C

Concept: The chord of the larger circle touches the smaller circle. Therefore, the perpendicular distance from the common center to the chord is equal to the radius of the smaller circle.

Step 1: Identify the given data. Radius of larger circle: \[ R=5\;cm \] Radius of smaller circle: \[ r=3\;cm \] Distance of chord from center: \[ d=3\;cm \]

Step 2: Use chord length formula. Length of chord: \[ L=2\sqrt{R^2-d^2} \] Substituting values: \[ L=2\sqrt{5^2-3^2} \] \[ L=2\sqrt{25-9} \] \[ L=2\sqrt{16} \] \[ L=2\times4 \] \[ L=8\;cm \] \centerline{{8 cm}}