Question

A circle has a chord that goes from `( 11 pi)/6` to `(7 pi) / 4` radians on the circle. If the area of the circle is `120 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=2.86`

Explanation:

The area of the circle is `=120pi`

Let the radius of the circle be `=r`

Then,

`pir^2=120pi`, `=>`, `r^2=120`, `r=sqrt120`

The angle subtended by the chord at the centre of the circle is

`theta=11/6pi-7/4pi=44/24pi-42/24pi=2/24pi=1/12pi`

The length of the chord is

`=2rsin(theta/2)=2*sqrt120sin(1/2*1/12pi)`

`=2.86`