Inscribed Equilateral

Geometry Level 3

Equilateral \(\Delta ABC\) with side length \(12\) is inscribed in a circle. Points \(D,E,F\) are on minor arcs \(\overset{\frown}{BC}\), \(\overset{\frown}{AC}\), and \(\overset{\frown}{AB}\), respectively, such that \(AD+BE+CF=40\). Find the perimeter of hexagon \(AECDBF\).

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