A circle has a chord that goes from #( pi)/3 # to #(7 pi) / 12 # radians on the circle. If the area of the circle is #36 pi #, what is the length of the chord?

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Answer 1 · 2016-11-25T18:09:48

The length of the chord, #c ~~ 4.59#

Given: #Area = 36pi#

Use #Area = pir^2# to solve for r:

#36pi = pir^2#

#r^2 = 36#

#r = 6#

Two radii, one each drawn to its respective end of the chord, form a triangle. The angle, C, between the radii is:

#C = (7pi)/12 - pi/3 = pi/4#

To find the length of the chord, c, we can use the Law of Cosines:

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

where #a = b = r = 6 and C = pi/4#

#c = sqrt(6^2 + 6^2 - 2(6)(6)cos(pi/4)#

#c ~~ 4.59#