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 `14 pi`, what is the length of the chord?

Answer 1

length of chord `=sqrt7(sqrt3-1)~~1.9368`

Explanation:

As area of a circle is given by `pir^2`, and it is `14pi`, we have `r=sqrt14`.

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*sqrt14*sin(pi/12)~~1.9368`

exact value:
`=2*sqrt14*((sqrt6-sqrt2)/4)`
=`sqrt21-sqrt7=sqrt7(sqrt3-1)`