Question

A circle has a chord that goes from `(2 pi)/3` to `(5 pi) / 8` radians on the circle. If the area of the circle is `6 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=0.32`

Explanation:

The area of the circle is `=6pi`

Let the radius of the circle be `=r`

Then,

`pir^2=6pi`, `=>`, `r^2=6`, `r=sqrt6`

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

`theta=2/3pi-5/8pi=16/24pi-15/24pi=1/24pi`

The length of the chord is

`=2rsin(theta/2)=2*sqrt6sin(1/2*1/24pi)`

`=0.32`