# Too many points!

Geometry Level 3

Alice has an equilateral triangle $$ABC$$ of area 1. Put $$D$$ on $$BC,$$ $$E$$ on $$CA,$$ and $$F$$ on $$AB,$$ with $$BD = DC, CE = 2EA,$$ and $$2AF = F B.$$ Note that $$AD, BE,$$ and $$CF$$ pass through a single point $$M.$$

If the area of the triangle $$EMC$$ can be expressed as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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