Question

In two concentric circles, the radii are $5$ cm and $13$ cm. If the chord of the circle of radius $13$ is the tangent to the circle of radius $5$ cm, then find the length of the chord of the bigger circle.

• A. $36$ cm
• B. $13$ cm
• C. $24$ cm
• D. $9$ cm

Answer 1

The correct option is C $24$ cm

Let radius of the smaller circle $=OC=r=5$ cm.
And radius of bigger circle $=OA=R=13$ cm.
Now in the smaller circle $OC=OP=5$ cm.
Since AB is the chord of the bigger circle, it is tangent to the smaller circle.
OP $\perp AB$ or $\angle OPA={90}^{\circ }$
Now in $\Delta OAP$,
$O{A}^2=O{P}^2+A{P}^2$
$\Rightarrow {13}^2=5^2+A{P}^2$
$\Rightarrow A{P}^2=144\Rightarrow AP=12cm$
$\therefore AB=2AP=2\times 12=24cm.$