A circle has a chord that goes from #( 3 pi)/2 # to #(7 pi) / 4 # radians on the circle. If the area of the circle is #196 pi #, what is the length of the chord?

1 Answer
Douglas K.
Oct 5, 2016

The chord is #~~10.7#

Explanation:

Use the area to compute the radius:

#A = pir²#

#196pi = pir²#

#r² = 196#

#r = 14#

The angle, #theta# between two radii, one to each end of the chord is:

#theta = 7pi/4 - 3pi/2 = pi/4#

Because the two radii and the chord form a triangle we can use the Law of Cosines:

#c² = a² + b² + 2(a)(b)cos(C)#

where #a = b = r = 14# and #C = theta = pi/4

#c² = 14² + 14² - 2(14)(14)cos(pi/4)#

#c ~~ 10.7#

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