Question

A circle has a chord that goes from `pi/4` to `pi/2` radians on the circle. If the area of the circle is `9 pi`, what is the length of the chord?

Answer 1

The length of the chord is `=2.3u`

Explanation:

The angle subtented at the center of the circle is

`theta=1/2pi-1/4pi=1/4pi`

The area of the circle is

`A=pir^2`

So, the radius is

`r=sqrt(A/pi)=sqrt(9pi/pi)=3`

The length of the chord is

`AB=2*AC=2*r*sin(theta/2)`

`=2*3*sin(1/8pi)`

`=2.3`