If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other is

1. 3 cm

2. 6 cm

3. 9 cm

4. 1 cm

From figure,

AB is chord to the bigger circle which is tangent to the smaller circle at C.

OC ⊥ AC (∵ radius of a circle and tangent through that point are perpendicular to each other.)

∴ ∠ACO = 90°.

In △ACO,

$\Rightarrow OA^2 = OC^2 + AC^2 \\[1em] \Rightarrow 5^2 = 4^2 + AC^2 \\[1em] \Rightarrow 25 = 16 + AC^2 \\[1em] \Rightarrow 25 - 16 = AC^2 \\[1em] \Rightarrow AC^2 = 9 \\[1em] \Rightarrow AC = 3 \text{ cm}.$

Length of chord AB = 2 × AC = 2 × 3 = 6 cm.

Hence, Option 2 is the correct option.