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?

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Answer 1 · 2018-01-04T11:05:59

Length of the chord = 7.0711

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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#