HMMT 2012 G8

Hexagon $A B C D E F$ has a circumscribed circle and an inscribed circle. If $A B=9, B C=6, C D=2$ , and $E F=4$ . Find $\{D E, F A\}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\left{\frac{9+\sqrt{33}}{2}, \frac{9-\sqrt{33}}{2}\right}

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