Question

A circle has a chord that goes from `( 5 pi)/3` to `(17 pi) / 12` radians on the circle. If the area of the circle is `27 pi`, what is the length of the chord?

Answer 1

`=> "chord length "~~3.977` to 3 decimal places

Explanation:

The angle of the arc is `|(17/12-5/3)pi|=|-1/4 pi| = 1/4 pi`

`pi-=180^o; 1/2pi-=90^o; 1/4pi-= 45^o`

Let the radius be `r`

`color(blue)("To determine the radius")`

Known: area`=pi r^2`

`=>27pi=pi r^2`

Divide both sides by `pi`

`=>27=r^2`

`=>r=sqrt(27) =sqrt(3xx9)=sqrt(3xx3^3)`

`r=3sqrt(3)`

Thus the chord length `= 2xx3sqrt(3)xxcos(3/8 pi)`

`=> r~~3.977` to 3 decimal places