Question

A chord with a length of `1` runs from `pi/12` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

Area of the circle `A_c =color(green)(~~ 28.2743` sq units

Explanation:

In the figure above,

`AhatOB = theta = pi/2 - pi/12 = (5pi)/12, AM = (AB) / 2 = 1/2`

`vec(OA) = r = (AM) / sin (theta/2) = (1/2) / sin ((5pi)/24) ~~ 0.3`

Area of the circle `A_c = pi r^2 = pi * 3^2 = color(green)(~~ 28.2743` sq units