A circle has a chord that goes from #( 5 pi)/8 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?

1 Answer
Douglas K.
Aug 24, 2017

#c ~~ 7.17#

Explanation:

Use the formula

#"Area" = pir^2#

to find the value of r:

#16pi = pir^2#

#r^2 = 16#

#r = 4#

The angle between two radii to each end of the chord is:

#theta = (4pi)/3-(5pi)/8#

#theta = (17pi)/24#

Because the two radii and the chord form a triangle we can use The Isosceles case of The Law of Cosines to find the length of the chord, c:

#c^2 = 2r^2(1-cos(theta))#

#c = sqrt(2(4)^2(1 - cos((17pi)/24)))#

#c ~~ 7.17#

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