Question

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

• A. $3$ cm
• B. $6$ cm
• C. $4$ cm
• D. None of these

Answer 1

Answer: (A)

$3$ cm

Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let radius of the circle is r cm.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

since OP is perpendicular to AB and OQ is perpendicular to CD and AB || CD

From figure, OP = 4 cm.

P, Q are the mid points of AB and CD. [perpendicular from centre bisect the chord]

So$AP=PB=\frac{AB}{2}=\frac{6}{2}=3cm$

$CQ=QD=\frac{CD}{2}=\frac{8}{2}=4cm$

Now in triangle OAP

${OA}^2={OP}^2+{AP}^2$

$r^2=16+9$

$r=\sqrt{16+9}$

$r=5cm$

Again from triangle OCQ

${OC}^2={OQ}^2+{CQ}^2$

$r^2={OQ}^2+16$

$25={OQ}^2+16$

${OQ}^2=25-16$

${OQ}^2=9$

$OQ=\sqrt{9}$

$OQ=3cm$

The distance of other chords from the centre is 3cm.

Therefore option $A$ is the answer.