Question

A circle has a chord that goes from `( pi)/2` to `(11 pi) / 6` radians on the circle. If the area of the circle is `25 pi`, what is the length of the chord?

Answer 1

Length of the chord = 7.0711

Explanation:

Area of the circle `A = pi R^2 = 25 pi`

`R = sqrt((25 pi ) / pi) = 5`

Angle subtended by the chord at the center

`theta = ((11pi)/6) - ((pi)/2) = (8pi)/6`

`C / 2 = R * sin (theta/2)`

`C =2 * 5 * sin ((8pi) / 12) = 7.0711`