Question

A circle has a chord that goes from `( 3 pi)/8` to `(5 pi) / 3` radians on the circle. If the area of the circle is `48 pi`, what is the length of the chord?

Answer 1

The length of the chord is `2Rsin(beta/2)` where `R` is the radius of the circle and `beta` is the angle at the center.

Explanation:

If the area of the circle is `48pi` the radius is:

`piR^2 = 48pi => R=sqrt(48)`

The angle at the center is:

`beta = (5pi)/3 -(3pi)/8 =(31pi)/24`

The length of the chord is:

`L =2sqrt(48)sin((31pi)/48)`