Q : 3  The lengths of two parallel chords of a circle are and . If the smaller chord is at distance from the centre, what is the distance of the other chord from the centre?

Given : AB = 8 cm, CD = 6 cm , OM = 4 cm and AB || CD.

To find: Length of ON

Construction: Draw

Proof :

Proof: CD is a chord of circle  and

Thus, CM = MD = 3 cm    (perpendicular from centre bisects chord)

and      AN = NB  = 4 cm

Let MN be x.

So, ON = 4 - x              (MN = 4 cm )

In  OCM , using Pythagoras,

.............................1

and

In  OAN , using Pythagoras,

.............................2

From 1 and 2,

So, x=1  (since  )

ON =4-x =4-1=3 cm

Hence, second chord is 3 cm away from centre.

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