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 C be the center of concentric circles and AB be the chord of larger circle touching smaller circle at point D.

So, AB can be the tangent to smaller circle.

We know that,

The tangent at any point of a circle is perpendicular to the radius through the point of contact.

∴ CD ⊥ AB.

In right angle triangle ACD,

By pythagoras theorem,

⇒ AC² = AD² + CD²

⇒ 5² = AD² + 3²

⇒ AD² = 25 - 9

⇒ AD² = 16

⇒ AD = $\sqrt{16}$ = 4 cm.

In △DAC and △DBC,

⇒ ∠CDA = ∠CDB (Both equal to 90°)

⇒ AC = BC = 5 cm

⇒ CD = CD (Common)

∴ △DAC ≅ △DBC (By SAS axiom)

∴ AD = BD (By C.P.C.T.)

∴ BD = 4 cm.

AB = AD + BD = 4 + 4 = 8 cm.

Hence, length of required chord = 8 cm.