An Inscribed Hexagon

Geometry Level 3

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

If the length of chord ADAD is mn \frac{ m}{n} , where mm and nn are relatively prime integers, find m+nm + n .

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