Q: 2 Two chords AB and CD of lengths and respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is , find the radius of the circle.
Given : AB = 5 cm, CD = 11 cm and AB || CD.
To find Radius (OA).
Construction: Draw
Proof :
Proof: CD is a chord of circle and
Thus, CM = MD = 5.5 cm (perpendicular from centre bisects chord)
and AN = NB = 2.5 cm
Let OM be x.
So, ON = 6 - x (MN = 6 cm )
In OCM , using pythagoras,
.............................1
and
In OAN , using pythagoras,
.............................2
From 1 and 2,
(OC=OA =radii)
From 2, we get
OA = OC
Thus, the radius of the circle is