Question

A circle has a chord that goes from `( pi)/3` to `(2 pi) / 3` radians on the circle. If the area of the circle is `96 pi`, what is the length of the chord?

Answer 1

Lengthof chord `=4sqrt6`

Explanation:

From the area, we calculate the radius `r^2pi=96pi`
so `r^2=96` and `r=4sqrt6`
The angle at the center is `theta=(2pi)/3-pi/3=pi/3`
The length of the chord is `2rsin(theta/2)=2*4sqrt6*sin pi/6=(8sqrt6)/2=4sqrt6`