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

विकल्प

• 6 cm

• \[5\sqrt{2} cm\]

   

•  7 cm

• \[3\sqrt{5} cm\]

   

Answer 1

\[3\sqrt{5}cm\]

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,

`x^2 + 36 = r^2` …… (1)

Now, in triangle AOM,

 `r^2 = 9 + (x +3)^2` …… (2)

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

`r^2 = 9 + (sqrtr^2 - 36 + 3)^2`

`⇒ r^2 = 9 + r^2 - 36 + 9 + 6 sqrt(r^2 - 36 )`

`⇒ 3 = sqrt(r^2 - 36)`

`⇒9 = r^2 - 36`

`⇒r^2 = 45 ⇒ r =3sqrt(5)`