A circle has a chord that goes from ( pi)/6 to (5 pi) / 6 radians on the circle. If the area of the circle is 135 pi , what is the length of the chord?

1 Answer
CW
Mar 2, 2017

Length of chord = 9sqrt5 ~~ 20.125

Explanation:

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As area of a circle is given by pir^2, and it is 135pi, we have r=sqrt135=3sqrt15

As shown in the figure, the angle Theta subtended by the chord at the centre is :
Theta=(5pi)/6-pi/6=(2pi)/3
=> Theta/2=pi/3
=> AM=rsin(Theta/2)
=> Length of chord AB=2*AM=2*r*sin(Theta/2)
=2*3sqrt15*sin(pi/3)=2*3sqrt15*sqrt3/2=9sqrt5

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