AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If chords are on opposite sides of the centre of the circle and distance between them is 17 cm find the radius of the circle.
 

Let AB and CD be two parallel chords of the circle C(O, r). Draw OE ⊥ AB and OF ⊥ CD since AB || CD, hence points E, O and F will be collinear, and EF = 17 cm.
Let OE = x cm, then OF = (17 - x) cm. Join 0B and OD.
This follows OB = OD = r
Again EB = AB = 5 cm
and FD = CD = 12 cm
In ΔOEB, ∠E = 90°
∴OB²  = OE² + EB² = x² + 25          .................... (i)
and OD² = OF² + FD² = (17 - x)² + 144   .................... (ii)
But OB = OD ⇒ OB² = OD²
From Equations (i) and (ii) we get,
x² + 25 = (17 - x)² + 144 ⇒ x = 12       
Substituting x = 12 in Equation (i).
We get r² = 169 ⇒ r = 13 cm
∴ The radius of the circle = 13 cm