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Let a triangle $\triangle ABC$. Assume $D,E,F$ points on sides $BC,CA,AB$ respectively such that $BD:DC = CE:EA = AF:FB = 4:1$. Here, $\triangle DEF$ is also a equilateral triangle. Given that, $\frac{[DEF]}{[ABC]}=\frac ab$ and $a,b$ are coprime. Find the value of $a+b$.

Geometry   BdMO  


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