Question

A chord with a length of `16` runs from `pi/3` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

Area of the circle = 13.4692

Explanation:

Given `/_(AOB )= pi/2 - pi/3 = (pi)/6`

`/_ (AOM) = /_ (AOB) / 2 = ((pi)/6) / 2 = (pi)/12`

`AB = 16, :. AM = 16/2 = 8`

Radius `OA = r = AM * sin /_AOM = 8 * sin ((pi)/12)`

Radius `r = 2.0706`

`Area = pi r^2 = pi * (2.0706)^2 = 13.4692`