Question

A circle has a chord that goes from `( pi)/6` to `(11 pi) / 8` radians on the circle. If the area of the circle is `64 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=15.2`

Explanation:

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

`theta=11/8pi-1/6pi=66/48pi-8/48pi=58/48pi=29/24pi`

Let the radius of the circle be `=r`

The area of the circle is `A=pir^2`

Here, `A=64pi`

So,

`pir^2=64pi`

`r^2=64`

`r=8`

The length of the chord is

`l=2*rsin(theta/2)`

`=2*8*sin(29/48pi)`

`=15.2`