Geometry

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.)

I've no idea how to do this, please help me out if you could!

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  1. If you did problem 1, then just subtract that from the area of the whole circle.

    If not, let's do it now. Recall that the area of the smaller segment is

    a = 1/2 r^2 (θ-sinθ)

    So, what's θ? Draw your diagram, and you can easily see that

    sin(θ/2) = 4/8 = 1/2
    θ = π/3

    Plug that into the formula, and you will have the area of the smaller segment.

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  2. Given a circle with an 8" radius, find the area of the smaller segment whose chord is 8" long

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