Question

A circle has a chord that goes from `( 2 pi)/3` to `(17 pi) / 12` radians on the circle. If the area of the circle is `9 pi`, what is the length of the chord?

Answer 1

Length of chord is `6sin((3pi)/8)`

Explanation:

Central angle `=(17pi)/12-(2pi)/3=(17pi)/12-(8pi)/12=(9pi)/12=(3pi)/4`
Half central angle`=(3pi)/8`
If area of circle is `9pi` then we calculate the radius
`pir^2=9pi` so `r^2=9` and `r=3`
Length of chord =`2rsin(theta/2)` where `theta` is the central angle
So length of chord `=2*3*sin((3pi)/8)=6sin((3pi)/8)`