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?

1 Answer
sankarankalyanam
Oct 19, 2017

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

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