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

If a chord is 8'' long then α = 60° = π/3 (the angle between the line segments connecting the ends of the chord and the center of the circle).

A = 1/2 r² (α - sin α) = 1/2 · 8² (π/3 - sin π/3) =

= 1/2 · 64 (1.046 - 0.866) = 5.76 in²

Answer: The area of a segment is 5.76 in²