Asked by Panda
Find the area of a segment formed by a chord 8" long in a circle with radius of 8".
Answers
Answered by
Steve
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.
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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