Question

A circle has a chord that goes from `( pi)/3` to `(5 pi) / 12` radians on the circle. If the area of the circle is `16 pi`, what is the length of the chord?

Answer 1

length of chord `~~1.04`

Explanation:

As area of a circle is given by `pir^2` and it is `16pi`, we have `r=sqrt16=4`.

As shown in the figure, the angle `Theta` subtended at the centre by the chord is `(5pi)/12-pi/3=pi/12`

`=> AM=rsin(Theta/2)`
`=>` length of chord `=AB=2AM=2rsin(Theta/2)`
`=2*4*sin(pi/24)=1.04` (2dp)