Question

The radius of two concentric circles is $8 \mathrm{~cm}$ and $17 \mathrm{~cm}$ respectively. If the chord of the largest circle touches the smallest circle externally then find the length of the largest chord.

• A. $32 \mathrm{~cm}$
• B. $28 \mathrm{~cm}$
• C. $30 \mathrm{~cm}$
• D. None

Answer 1

Answer: (C)

Let ' $O$ ' be the centre of circle and $P Q$ is the chord of the largest circle.

Here, $O P=17 \mathrm{~cm}$ and $O R=8 \mathrm{~cm}$,
In right $\triangle O R P, \angle R=90^{\circ}$
By using Pythagoras theorem,
$(O P)^2 =(O R)^2+(P R)^2 $
$\Rightarrow(17)^2 =(8)^2+(P R)^2$
$ \Rightarrow(P R)^2=289-64 \Rightarrow(P R)^2=225$
$ \Rightarrow P R=15 \mathrm{~cm} \Rightarrow P Q=2(P R)$
$\Rightarrow P Q=2(15)=30 \mathrm{~cm}$