A circle has a chord that goes from #( pi)/3 # to #(7 pi) / 8 # radians on the circle. If the area of the circle is #24 pi #, what is the length of the chord?

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Answer 1 · 2016-06-10T09:01:15

It is #7.36#.

The length of a chord is given by

#c=2rsin(\theta/2)# where #theta# is the angle under the chord and #r# is the radius of the circle.

We start calculating the radius. We have the area that is #24\pi# and we know that the area of the circle is

#A=pir^2#, then the radius is

#r=sqrt(A/pi)=sqrt(24)\approx4.9#

Then we have to calculate the angle. It is simply the difference between the final angle and the initial angle

#\theta=7/8pi-pi/3=(21-8)/24pi=13/24pi#

So the length of the chord is

#c=2rsin(\theta/2)#

#=2*4.9*sin(1/2*13/24pi)#

#=9.8*sin(13/48pi)#

#=7.36#.

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