Question

Two concentric circles are of radii $5cm$ and $3cm$. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

Let $O$ be the centre of the concentric circle of radii $5$ cm and $3$ cm respectively. Let $AB$ be a chord of the larger circle touching the smaller circle at $P$.

Then

$AP=PB$ and $OP\perp AB$

Applying Pythagoras theorem in $△OPA$, we have
${OA}^2={OP}^2+{AP}^2$

$\Rightarrow 25=9+{AP}^2$

$\Rightarrow {AP}^2=16\Rightarrow AP=4cm$

$\therefore AB=2AP=8cm$