Two chords AB and CD of lengths 5 cm and 11 cm 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 6 cm, find the radius of the circle.
Draw OM perpendicular AB and ON perpendicular CD
Join OB and OD
BM = 
(The perpendicular drawn from the center bisects the chord)
Let ON be x
Therefore, OM will be 6 –x
In ΔMOD,
OM2 + MB2 = OB2
(6 – x)2 + 
2 = OB2
36 + x2 -12x + 
OB2 (i)
In ΔNOD,
ON2 + ND2 = OD2
(x)2 + 
2 = OD2
(x)2 + 
= OD2 (ii)
We have OB = OD (radii of the same circle)
Therefore,
From (i) and (ii),
36 + x2 -12x + 
(x)2 + 
36 -12x + 
x = 1
From (ii),
(1)2 + 
= OD2
OD = 
cm
5