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?

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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

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Answer 1 · 2016-10-16T08:16:35

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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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

Explanation:

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