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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