Leave answer in exact form unless otherwise indicated.

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

Area segment = 32/3 π - 16√3 inches²

Step-by-step explanation:

∵ The length of the chord is 8"

∵ The length of the radius of the circle is 8"

∴ the central angle of the segment is π/3 (60° the chord and the radii

   formed an equilateral triangle)

∵ The area of the segment = area the sector - area Δ

∵ Area sector = 1/2 r²Ф

∵ r = 8" and Ф = π/3

∴ Area sector = 1/2 (8²) (π/3) = 32/3 π inches²

∵ Area Δ = 1/4 s²√3

∵ The length of the side is 8"

∴ Area Δ = 1/4 (8²) √3 = 16√3 inches²

∴ Area segment = 32/3 π - 16√3 inches²