Question

In two concentric circle, a chord of length 24 cm. Find the radius of the larger circle.

Answer 1

Let $O$ be the centre of concentric circles and $APB$ be the chord of length $24$ cm, of the larger circle touching the smaller circle at $P$.

Then, $OP\perp AB$ and $P$ is the mid-point of $AB$.

$\therefore AP=PB=12$ cm

In $△OPA$, we have

${OA}^2={OP}^2+{AP}^2$ [by pythagorus theorem]

$\Rightarrow {OA}^2=5^2+{12}^2=169$

$\Rightarrow OA=13$ cm

Hence, the radius of the smaller circle is $13$ cm.