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?

1 Answer
sankarankalyanam
Jan 4, 2018

Length of the chord = 7.0711

Explanation:

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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

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