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 O be the centre of two concentric circles with radius 5 cm (OP) and 3 cm (OA). PQ is chord of larger circle which is a tangent to inner circle.
We know that the radius is perpendicular to tangent. Therefore, in ΔPQO, OA ⊥PQ.
In ΔAPO, by Pythagoras theorem,
OA² + AP² = OP²
⇒ 3² + AP² = 5²
⇒ 9 + AP² = 25 ⇒ AP² = 16 ⇒ AP = 4
In ΔOPQ, OA ⊥ PQ
AP = AQ [Perpendicular from the centre bisects the chord]
So, PQ = 2AP = 2 × 4 = 8
Hence, the length of chord of larger circle is 8 cm.