A circle has a chord that goes from ( pi)/2 to (3 pi) / 4 radians on the circle. If the area of the circle is 96 pi , what is the length of the chord?

1 Answer
CW
Apr 7, 2017

length of chord ~~ 7.499

Explanation:

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Area of a circle A=pir^2,
Given A=96pi, => r=sqrt96

As shown in the figure, the angle theta subtended by the chord at the centre is :
theta=(3pi)/4-pi/2=pi/4
=> theta/2=pi/8

=> AM=rsin(theta/2)

=> length of chord AB=2AM=2*r*sin(theta/2)
= 2*sqrt96*sin(pi/8)~~7.499

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