Solution:

Two concentric circles with center O

OP and OB are the radii of the circles respectively, then

OP = 5 cm, OB = 13 cm.

Ab is the chord of outer circle which touches the inner circle at P.

OP is the radius and APB is the tangent to the inner circle.

In the right angled triangle OPB, by Pythagoras axiom,

OB² = OP² + PB²

13² = 5² + PB²

169 = 25 + PB²

PB² = 169 – 25

= 144

PB = 12 cm

But P is the mid-point of AB.

AB = 2PB

= 24 cm