Question

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

Answer 1

Chord length is `1.5528`

Explanation:

As area of a circle is given by `pir^2` and it is `9pi`, we have `r=sqrt9=3`.

Now see the given figure. The angle subtended by the chord at the center is `pi/2-pi/3=pi/6`.

If the chord length is `a` and angle subtended by the chord at the center is `theta`, the relation we have is

`sin(theta/2)=(a/2)/r` or `a=2rsin(theta/2)`

Hence, chord length is `2xx3xxsin(pi/12)=6xx0.2588=1.5528`