# Triangles and areas

Geometry Level 5

In a triangle $$ABC$$, let $$G$$ denote its centroid and let $$M$$, $$N$$ be points in the interiors of the segments $$AB$$,$$AC$$,respectively, such that $$M$$, $$G$$, $$N$$ are collinear. If $$r$$ denotes the ratio of the area of triangle $$AMN$$ to the area of $$ABC$$ and $$r_{min}=\frac{a}{b}$$ (a and b are co-prime natural numbers.). Find the value of $$a+b$$

NOTE:-This question was asked in KVPY-2013

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