Question

$PQ$ and $RS$ are two parallel chords of a circle such that $PQ=10cm$ & $RS=24cm$. If the chords are on the opposite sides of the centre and the distance between them is $17cm$, find the radius of the circle.

• A. 14 cm
• B. 10 cm
• C. 13 cm
• D. 15 cm

Answer 1

Correct option is B. 13 cm

Let $OM\perp PQ$ and $ON\perp RS$.Therefore,

$\Rightarrow PM=MQ=\frac{10}{2}=5cm$ and

$\Rightarrow PN=SN=\frac{24}{2}=12cm$

Since, $MN=17cm$ (distance between the parallel chords), let $OM=x$. Therefore, $ON=17-x$

Consider right $\Delta PMO$. By Pythagoras Theorem,

$\Rightarrow P{O}^2=M{O}^2+P{M}^2$

$\Rightarrow P{O}^2=x^2+5^2$..(i)

Consider right $\Delta RNO$. By Pythagoras Theorem,

$\Rightarrow R{O}^2=N{O}^2+R{N}^2$

$\Rightarrow R{O}^2=(17-x{)}^2+{12}^2$...(ii)

Since, radii of circle are equal, therefore, $P{O}^2=R{O}^2$

From (i) and (ii),

$\Rightarrow x^2+5^2=(17-x{)}^2+{12}^2$

$\Rightarrow x^2+25=289+x^2-34x+144$

$\Rightarrow 408=34x$

$\Rightarrow x=12$

$\therefore PO=\sqrt{{12}^2+5^2}=13cm$

Hence, radius of the circle is $13cm$.