A circle has a chord that goes from #( 5 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?

1 Answer
Tony B
May 10, 2016

#=> "chord length "~~3.977# to 3 decimal places

Explanation:

The angle of the arc is #|(17/12-5/3)pi|=|-1/4 pi| = 1/4 pi#

#pi-=180^o; 1/2pi-=90^o; 1/4pi-= 45^o#

Let the radius be #r#

Tony B
#color(blue)("To determine the radius")#

Known: area#=pi r^2#

#=>27pi=pi r^2#

Divide both sides by #pi#

#=>27=r^2#

#=>r=sqrt(27) =sqrt(3xx9)=sqrt(3xx3^3)#

#r=3sqrt(3)#

Thus the chord length #= 2xx3sqrt(3)xxcos(3/8 pi)#

#=> r~~3.977# to 3 decimal places

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