Question

A chord with a length of `1` runs from `pi/8` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

Area of the circle `= color (purple)(0.2424)`

Explanation:

Given `/_(AOB )= pi/2 - pi/8 = (3pi)/8`

`/_ (AOM) = /_ (AOB) / 2 = ((3pi)/8) / 2 = (3pi)/16`

`AB = 1, :. AM = 1/2`

Radius `OA = r = AM * sin /_AOM = (1/2) * sin ((3pi)/16)`

Radius `r = 0.2778`

`Area = pi r^2 = pi * (0.2778)^2 =0.2424`