A circle has a chord that goes from #pi/3 # to #pi/2 # radians on the circle. If the area of the circle is #9 pi #, what is the length of the chord?

1 Answer
Shwetank Mauria
Nov 7, 2016

Chord length is #1.5528#

Explanation:

As area of a circle is given by #pir^2# and it is #9pi#, we have #r=sqrt9=3#.

Now see the given figure. The angle subtended by the chord at the center is #pi/2-pi/3=pi/6#.
enter image source here
If the chord length is #a# and angle subtended by the chord at the center is #theta#, the relation we have is

#sin(theta/2)=(a/2)/r# or #a=2rsin(theta/2)#

Hence, chord length is #2xx3xxsin(pi/12)=6xx0.2588=1.5528#

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