Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of the larger circle which touches the smaller circle is:

24 cm

We know that,

Hypotensue² = Base² + Perpendicular²

OM = 5

OP = 13

In ΔOPM

(OP)² = (OM)² + (PM)²

= 13² = 5² + (PM)²

= (PM)² = 169 - 25 

= PM = $\sqrt {144}$

= PM = 12

Now,

PQ = 2PM

= PQ = 2 × 12

= PQ = 24 cm