Geometry
posted by Panda .
Find the area of a segment formed by a chord 8" long in a circle with radius of 8".

as we all know, the side of an inscribed hexagon is equal to the radius.
So, the angle subtending the side is π/3
a = 1/2 r^2 (θ  sinθ)
= 1/2 * 64 (π/3  √3/2)
= 32/6 (2π  3√3)
More generally, the angle θ which subtends a chord of length s in a circle of radius r is
sin θ/2 = (s/2)/r = s/2r
In this problem, s=r=8, so
sin θ/2 = 1/2
θ = π/3
and away we go.
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