Question

A chord with a length of `15` runs from `pi/8` to `pi/3` radians on a circle. What is the area of the circle?

Answer 1

Area of the circle `A_c = pi r^2 = pi (23.3325)^2 = color (purple)(1710.3)` sq. units

Explanation:

Length of the chord `L_c = 15` given

Center angle subtended by the chord `theta = (pi/3) - (pi/8) = (5pi)/24`

`theta / 2 = ((5pi)/48)`

Radius of the circle `r = L_c / (2*sin (theta/2) )= 15 / (2 * sin ((5pi)/48) )= color (red)(23.3325)`

Area of the circle `A_c = pi r^2 = pi (23.3325)^2 = color (purple)(1710.3)` sq. units