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 radius of the circle is?

• A. $10$ cm
• B. $5$ cm
• C. $3$ cm
• D. None of these

Answer 1

The correct option is B $5$ cm

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

Let the radius of the circle be r.

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 respectively. [perpendicular from center bisects 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

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

$r^2=16+9$

$r=\sqrt{16+9}$

$r=5cm$

So, option $B$ is the answer.