A circle has a chord that goes from #( 11 pi)/6 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #120 pi #, what is the length of the chord?

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Answer 1 · 2017-06-07T13:27:26

The length of the chord is #=2.86#

The area of the circle is #=120pi#

Let the radius of the circle be #=r#

Then,

#pir^2=120pi#, #=>#, #r^2=120#, #r=sqrt120#

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

#theta=11/6pi-7/4pi=44/24pi-42/24pi=2/24pi=1/12pi#

The length of the chord is

#=2rsin(theta/2)=2*sqrt120sin(1/2*1/12pi)#

#=2.86#