A geometry problem by Deepansh Jindal

Geometry Level 4

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.

Give your answer correct to 2 decimal places.

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