A circle has a chord that goes from ( 2 pi)/3 to (17 pi) / 12 radians on the circle. If the area of the circle is 9 pi , what is the length of the chord?

1 Answer
Narad T.
Oct 16, 2016

Length of chord is 6sin((3pi)/8)

Explanation:

Central angle =(17pi)/12-(2pi)/3=(17pi)/12-(8pi)/12=(9pi)/12=(3pi)/4
Half central angle=(3pi)/8
If area of circle is 9pi then we calculate the radius
pir^2=9pi so r^2=9 and r=3
Length of chord =2rsin(theta/2) where theta is the central angle
So length of chord =2*3*sin((3pi)/8)=6sin((3pi)/8)

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