Question

$AB$ and $CD$ are two parallel chords of a circle such that $AB=10cm$ and $CD=24cm$, if the chords are on the opposite sides of the centre and the distance between them is $17cm$, then the radius of the circle is

• A. $8cm$
• B. $13cm$
• C. $11cm$
• D. $12cm$

Answer 1

The correct option is B $13cm$

Let $OP$ be $xcm$ and radius be $rcm$.
$\therefore OQ=(17-x)cm$
$\therefore In△OQC$,
$(OC{)}^2=(OQ{)}^2+(QC{)}^2$
$r^2=(17-x{)}^2+(12{)}^2.....\left(1\right)$
and in $△OAP$,
$(OA{)}^2=(OP{)}^2+(AP{)}^2$
$r^2=x^2+5^2....\left(2\right)$
On equating equation $\left(1\right)$ and $\left(2\right)$,
$\therefore (17-x{)}^2+(12{)}^2=x^2+5^2$
$\Rightarrow 289-34x+x^2+144=x^2+25\Rightarrow 34x=408$
$\therefore x=12cm$
$r^2=x^2+5^2=(12{)}^2+(5{)}^2=144+25=169\Rightarrow r=13cm$.