# Look at it in another way

Geometry Level 3

In the diagram, $$\triangle{ABC}, \triangle{CDE}, \triangle{EFG}$$ and $$\triangle{HGI}$$ are congruent isosceles triangles. $$B,C,E,G$$ and $$I$$ are collinear. Suppose that $$\overline{AC}$$ and $$\overline{BH}$$ meet at $$M$$ and $$\overline{FG}$$ and $$\overline{BH}$$ meet at $$N$$. Given $$[HGN]=10$$, then the value of $$[BMC]$$ is $$\frac{m}{n}$$ for relatively prime $$m$$ and $$n$$. Find $$m+n$$.

$$[ABC]$$ denotes the area of figure $$ABC$$.

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