Question

AB and CD are two chords of a circle such that AB=6cm, CD=12cm and ABllCD. If the distance between AB and CD is 3cm, find the radius of the circle.

Answer 1

Answer:

Let AB and CD be two parallel chords of a circles with centre O such that AB = 6cm and CD = 12cm. Let the radius of the circle be r cm. Draw OP $\perp$ AB and OQ$\perp$CD. Since AB || CD and OP $\perp$ AB, OQ $\perp$ CD. Therefore, point O, Q, P are collinear.

Clearly, PQ = 3cm

$\leadsto$ Let OQ = x cm. Then, OP = (x+3) cm

In right triangles OAP and OCQ, we have

OA² = OP² + AP² and OC² = OQ² + CQ²

= r² = (x+3)² + 3² and r² = x² + 6²

= (x+3)² + 3² = x² + 6²

=> x² + 6³ + 9 + 9 = x² + 36

= 6x = 18

=> x = 3cm.

Putting the value of x in r² = x² + 6², we get

r² = 3² + 6² = 45

r = √45 cm

r = 6.7 cm