Question

The length of two parallel chords of a circle are $6$ cm and $8$ cm. If the smaller chord is at a distance of $4$ cm from the centre, what is the distance of the other chord from the centre ?

Answer 1

$AB=6cm,CD=8cm$

Let $OL\perp AB$ and $OM\perp CD$

$\therefore OL=4cm$

Let $OM=xcm$

Let $r$ be the radius of the circle

Now in right $\Delta OAL$

$O{A}^2=O{L}^2+A{L}^2=4^2+{\left(\frac{6}{2}\right)}^2$

$r^2=16+9=25$ ............(i)

and in right $\Delta OMC$,

$O{C}^2=O{M}^2+C{M}^2$

$r^2=x^2+{\left(\frac{8}{2}\right)}^2$

$=x^2+(4{)}^2=x^2+16$ ............(ii)

From (i) and (ii),

$x^2+16=25$

$\Rightarrow x^2=25-16=9$

$\Rightarrow x^2=(3{)}^2$

$\therefore x=3cm$

$\therefore Distance=3cm$