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,
(OC=OA =radii)
So, x=1 (since )
ON =4-x =4-1=3 cm
Hence, second chord is 3 cm away from centre.