Question

If AB = 6 cm., CD = 12 cm. are two chords of a circle and are parallel and lie
at same side of centre of circle. If distance between AB and CD is 3 cm., then
find radius of circle.​

Answer 1

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Circles

Perpendicular to a Chord through the Centre

The lengths of two parallel...

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Asked on January 17, 2020 by

Daizzy Khatri

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?

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ANSWER

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=

2

AB

=

2

6

=3cm

CQ=QD=

2

CD

=

2

8

=4cm

Now in triangle OAP

OA

2

=OP

2

+AP

2

r

2

=16+9

r=

16+9

r=5cm

So, option B is the answer.