Posted by **Panda** on Thursday, January 10, 2013 at 11:10am.

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

- Geometry -
**Steve**, Thursday, January 10, 2013 at 11:32am
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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