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 12 pi , what is the length of the chord?

1 Answer
Douglas K.
Dec 23, 2016

The length of the chord is 6.4

Explanation:

Given: The area of the circle is 12pi

The area of a circle is:

Area = pir^2

12pi = pir^2

r = sqrt(12)

If you draw a radius from the center to one end of the chord and a radius from the center to the other end of the chord, you have a triangle. The angle, theta, between the two radii is:

theta = (17pi)/12 - (2pi)/3 = (3pi)/4

We can use the Law of Cosines to find the length of the chord:

c = sqrt(a^2 + b^2 - 2(a)(b)cos(theta))

where a = b = r = sqrt(12) and theta = (3pi)/4

c = sqrt(12 + 12 - 2(12)cos((3pi)/4))

c = 6.4

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