AB and CD are two parallel chords of a circle which are on either sides of the centre. Such that AB = 10 cm and CD = 24 cm. Find the radius if the distance between AB and CD is 17 cm.

From Theorem: A circle with radius r and a chord of length l which is at distance d from the centre, follows the equation,

In the figure, AB = 10cm = l

.....(1)

And CD = 24cm

.....(2)

As Distance between the two chords = PQ = 17cm

We have OP + OQ = 17....(3)

Equating equations 1 and 2 we get,

From identity we get

(OP + OQ)(OP–OQ) = 119

Using equation 3 we get

OP – OQ = 7 ....(4)

Solving equation 3 and 4 we get

OP = 12cm

OQ = 5cm

From Theorem: A circle with radius r and a chord of length l which is at distance d from the centre, follows the equation,

Using this in Triangle APO we get

Hence the radius of the triangle is 14cm