A circle has a chord that goes from #( 3 pi)/8 # to #(5 pi) / 3 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?

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Answer 1 · 2016-11-25T15:13:14

The length of the chord is #2Rsin(beta/2)# where #R# is the radius of the circle and #beta# is the angle at the center.

If the area of the circle is #48pi# the radius is:

#piR^2 = 48pi => R=sqrt(48)#

The angle at the center is:

#beta = (5pi)/3 -(3pi)/8 =(31pi)/24#

The length of the chord is:

#L =2sqrt(48)sin((31pi)/48)#