MCQ

*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

#### Options

6 cm

- \[5\sqrt{2} cm\]
7 cm

- \[3\sqrt{5} cm\]

Advertisement Remove all ads

#### Solution

\[3\sqrt{5}cm\]

Let distance between the centre and the chord CD be

We have to find the radius of the following circle:

*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)`

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads