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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