A circle has a chord that goes from #(2 pi)/3 # to #(5 pi) / 8 # radians on the circle. If the area of the circle is #6 pi #, what is the length of the chord?

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Answer 1 · 2017-06-06T08:10:21

The length of the chord is #=0.32#

The area of the circle is #=6pi#

Let the radius of the circle be #=r#

Then,

#pir^2=6pi#, #=>#, #r^2=6#, #r=sqrt6#

The angle subtended by the chord at the centre of the circle is

#theta=2/3pi-5/8pi=16/24pi-15/24pi=1/24pi#

The length of the chord is

#=2rsin(theta/2)=2*sqrt6sin(1/2*1/24pi)#

#=0.32#