Question

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are opposite side of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Answer 1

Let AB and CD be two parallel chord of the circle with centre O such that AB = 5 cm, CD = 11 cm and PQ = 6 cm. Let the radius of the circle be cm.

Draw and as well as point O, Q, and P are collinear.

Clearly, PQ = 6 cm

Let OQ = x cm then

Join OA and OC, then

OA = OC = r

Nowand

So, and

In we have

…… (1)

And

…… (2)

From (1) and (2) we get

Putting the value of x in (1) we get,