Look at it in another way

Geometry Level 3

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

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

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