In two concentric circles, a chord of length 24cm of larger circle becomes a tangent to the smaller circle whose radius is 5cm. Then the radius of the larger circle is

Let O be the centre of concentric circles and APB be the chord of length 24cm, of the largest circle touching the smaller circle at P. Then $\mathrm{OP}\perp \mathrm{AB}$ and P is the mid – point of AB.

$\therefore \mathrm{AP}=\mathrm{PB}=12\mathrm{cm}$

In  $\mathrm{\Delta OPA}$, we have

$\begin{array}{l}{\mathrm{OA}}^2={\mathrm{OP}}^2+{\mathrm{AP}}^2\text{ [By Pythagoras Theorem] }\\ \Rightarrow {\mathrm{OA}}^2=5^2+{12}^2=169\\ \Rightarrow \mathrm{OA}=13\mathrm{cm}\end{array}$