Two concentric circles are drawn with radii 20 cm and 16 cm. What will be the length of a chord of the larger circle which is tangent to the smaller circle?

24 cm

As BOC is an right angled triangle at C

Using Pythagoras theorem

⇒ \( { BO}^{2 } \) = \( { CO}^{2 } \) + \( { BC}^{2 } \)

⇒ \( { 20}^{2 } \) = \( { 16}^{2 } \) + \( { BC}^{2 } \)

⇒ 400 = 256 + \( { BC}^{2 } \)

⇒ BC = \(\sqrt {400\; - \; 256 }\)

⇒ BC = \(\sqrt {144}\)

⇒ BC = 12 cm

Now, as the line divides in 2 parts,

⇒ AB = 2BC = 2(12) = 24cm

Therefore, the length of the chord is 24 cm.