A circle has a chord that goes from #pi/4 # to #pi/2 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?

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Answer 1 · 2017-07-18T06:16:16

The length of the chord is #=2.3u#

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The angle subtented at the center of the circle is

#theta=1/2pi-1/4pi=1/4pi#

The area of the circle is

#A=pir^2#

So, the radius is

#r=sqrt(A/pi)=sqrt(9pi/pi)=3#

The length of the chord is

#AB=2*AC=2*r*sin(theta/2)#

#=2*3*sin(1/8pi)#

#=2.3#