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 $PQ$ is the chord of the largest circle.

Here, $OP=17\mathrm{cm}$ and $OR=8\mathrm{cm}$,
In right $△ORP,\angle R=90^{\circ }$
By using Pythagoras theorem,
$(OP{)}^2=(OR{)}^2+(PR{)}^2$
$\Rightarrow (17{)}^2=(8{)}^2+(PR{)}^2$
$\Rightarrow (PR{)}^2=289-64\Rightarrow (PR{)}^2=225$
$\Rightarrow PR=15\mathrm{cm}\Rightarrow PQ=2(PR)$
$\Rightarrow PQ=2(15)=30\mathrm{cm}$