Question

A circle has a chord that goes from `pi/12` to `pi/4` radians on the circle. If the area of the circle is `32 pi`, what is the length of the chord?

Answer 1

length of chord `=4(sqrt3-1)~~2.928`

Explanation:

As area of a circle is given by `pir^2`, and it is `32pi`, we have `r=sqrt32`.

As shown in the figure, the angle `Theta` subtended by the chord at the centre is :
`Theta=pi/4-pi/12=pi/6`
`=> Theta/2=pi/12`

`=> AM=rsin(Theta/2)`

`=>` length of chord `AB=2AM=2*r*sin(Theta/2)`
`= 2*sqrt32*sin(pi/12)~~2.928`

exact value:
`AB=2*sqrt32*((sqrt6-sqrt2)/4)`
`=1/2(8sqrt3-8)`
=`4(sqrt3-1)`