# An Inscribed Hexagon

Geometry Level 3

An inscribed Hexagon has sides $$AF = FE = ED = 4$$, $$AB = BC = CD = 2$$. Furthermore, $$ADEF$$ and $$ADCB$$ are trapeziums.

If the length of chord $$AD$$ is $$\frac{ m}{n}$$, where $$m$$ and $$n$$ are relatively prime integers, find $$m + n$$.

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