A circle has a chord that goes from #pi/3 # to #pi/4 # radians on the circle. If the area of the circle is #49 pi #, what is the length of the chord?

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Answer 1 · 2017-12-20T13:50:22

The length of the chord is #=1.83u#

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The angle subtended at the center of the circle is

#hat(AOB)=theta=pi/3-pi/4=pi/12#

The area of the circle is

#A=pir^2=49pi#

Therefore,

The radius of the circle is

#r=sqrt49=7#

The length of the chord is

#AB=2*AC=2*AOsin(theta/2)#

#=2*7*sin(pi/24)#

#=14*0.13#

#=1.83u#