# Geometry - Inadequate Information #2

Geometry Level 5

As shown in the figure above, a circle is inscribed in quadrilateral $$ABCD,$$ where $$M$$ and $$N$$ are midpoints of $$\overline{AC}$$ and $$\overline{BD},$$ respectively, $$\overline{AB}=5, \overline{CD}=9$$ and $$\overline{AC}^2+\overline{BD}^2+4 \overline{MN}^2=218.$$

Find the value of $$\overline{BC}\times\overline{DA}.$$

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