International Mathematical Olympiad 1982 Problem 5

The diagonals $AC$ and $CE$ of the regular hexagon $ABCDEF$ are divided by the inner points $M$ and $N$, respectively, so that

$$\frac{AM}{AC} = \frac{CN}{CE} = r.$$

Determine $r$ if $B$, $M$, and $N$ are collinear.