Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner.

We know that,

The tangent at any point of a circle and the radius through this point are perpendicular to each other.

In right triangle OST, we have

⇒ OS² = OT² + ST²

⇒ 5² = 3² + ST²

⇒ ST² = 25 - 9

⇒ ST² = 16

⇒ ST = $\sqrt{16}$

⇒ ST = 4 cm.

Similarly, in right triangle OQT, we have

⇒ OQ² = OT² + QT²

⇒ 5² = 3² + QT²

⇒ QT² = 25 - 9

⇒ QT² = 16

⇒ QT = $\sqrt{16}$

⇒ QT = 4 cm.

From figure,

QS = ST + QT = 4 + 4 = 8 cm.

Hence, the length of a chord of the outer circle which touches the inner = 8 cm.