Question

A circle has a chord that goes from `( pi)/8` to `(7 pi) / 6` radians on the circle. If the area of the circle is `135 pi`, what is the length of the chord?

Answer 1

Length of the chord c = 23.1881

Explanation:

Area of the circle `= pi r^2 = 135pi`
`:. r^2 = 135, r = sqrt135 = 3sqrt15`

Angle sub tended by the chord `theta` at the center = `((7pi)/6) - (pi/8)`
`theta = (25pi)/24`
`theta/2 = (25pi)/48`

Let the chord length be c. Then,
`sin (theta /2) = (c/2) / r`
`sin ((25pi)/48) = c / (2 * 3sqrt15)`

`c = 6sqrt15 * sin ((25pu)/24) = 23.1881`