# A geometry problem by Deepansh Jindal

Geometry Level 5

The diagonals $$AC$$ and $$CE$$ of the regular hexagon $$ABCDEF$$ are divided by the inner points $$M$$ and $$N$$, respectively, so that $$\dfrac{AM }{AC} = \dfrac{CN}{CE} = r$$. Determine the value of $$r$$ if $$B, M$$ and $$N$$ are collinear.