Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Let we have two concentric circles with centre O as shown. Now, draw a chord AB in the larger circle, which touches the smaller circle at a point P, as shown in the below figure.

It is clear from the figure that AB is tangent to the smaller circle to point P.

Thus, OP ⊥ AB

Applying Pythagoras’ theorem to ΔOPA,

OA²= AP² + OP²

5² = AP² + 3²

AP² = 25 - 9

AP² = 16

AP = 4

Now, as OP ⊥ AB,

Since the perpendicular from the centre of the circle bisects the chord, AP will be equal to PB.

So, AB = 2AP = 2 × 4 = 8 cm

Thus, the length of the chord of the larger circle is 8 cm.