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

From the above diagram, AB is tangent to the smaller circle to point P.

∴ OP ⊥ AB

Using Pythagoras theorem in triangle OPA,

OA²= AP²+OP²

5² = AP²+3²

AP² = 25-9

AP = 4

Now, as OP ⊥ AB,

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

So, AB = 2AP = 2×4 = 8 cm

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