Question

A chord with a length of `13` runs from `pi/12` to `pi/2` radians on a circle. What is the area of the circle?

Answer 1

`color(brown)("Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"`

Explanation:

`"Given ; " hat (AOB) = pi/2 - pi/12 = (5pi)/12, vec(AB) = 13`

`hat (AOM) = hat (AOB) / 2 = (5pi)/24`

`bar(OA) = r = bar(AM) / sin (AOM) = (bar(AB)/2) / sin (AOM)`

`r = (13/2) / sin ((5pi)/24) = 10.68 " units"`

`"Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"`