Question

AB and CD are two parallel chords of a circle with centre O such that AB = 6 cm and CD = 12 cm. The chords are on the same side of the centre and the distance between them is 3 cm. The radius of the circle is

(a) 6 cm

(b) $5\sqrt{2}\mathrm{cm}$

(c) 7 cm

(d) $3\sqrt{5}\mathrm{cm}$

Answer 1

(d) $3\sqrt{5}\mathrm{cm}$

Let distance between the centre and the chord CD be x cm and the radius of the circle is r cm.

We have to find the radius of the following circle:

In triangle OND,

…… (1)

Now, in triangle AOM,

…… (2)

From (1) and (2), we have,

Hence, the correct answer is option (d).