SOLUTION: Express answer in exact form. Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius. (Hint: A chord divides a circle into two segments. In p

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Question 763264: Express answer in exact form.
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.
(Hint: A chord divides a circle into two segments. In problem 1, you found the area of the smaller segment.)

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Express answer in exact form.
Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.
:
We know that the triangle formed by the two radii and the chord is
an equilateral triangle, all angles are 60 degrees, which is 1/6 of
360 degrees
:
Find area inside the 60 degree arc
1%2F6*pi%2A8%5E2 = 35.51
:
Find the area of the equilateral triangle
1%2F2*8*sqrt%288%5E2-4%5E2%29 = 27.71 sq/in
:
Find the area of the shape enclosed by the 60 degree arc and the chord
35.51 - 27.71 = 7.8 sq/in
:
Find the area of the larger segment
pi%2A8%5E2 - 7.8 = 193.26 sq/inches