Inscribed Equilateral

Geometry Level 3

Equilateral ΔABC\Delta ABC with side length 1212 is inscribed in a circle. Points D,E,FD,E,F are on minor arcs BC\overset{\frown}{BC}, AC\overset{\frown}{AC}, and AB\overset{\frown}{AB}, respectively, such that AD+BE+CF=40AD+BE+CF=40. Find the perimeter of hexagon AECDBFAECDBF.

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