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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