Question

A chord with a length of `4` runs from `pi/12` to `pi/3` radians on a circle. What is the area of the circle?

Answer 1

Area of the circle `A_c = color (purple)(25.1327)`#

Explanation:

Given : Chord length `d = 4`

`delta = pi/3 - pi/12 = pi/4`

`R = d / (2 * sin delta) = 4 / (2 * sin (pi/4)) = 2sqrt2`

Area of circle #A_c = pi R^2 = pi * (2sqrt2)^2 = 8pi = color (purple)(25.1327)#