Geometry Level 4

In a $$\triangle ABC$$, points $$M$$ and $$N$$ are on sides $$AB$$ and $$AC$$ respectively, such that $$MB$$ $$=$$ $$BC$$ $$=$$ $$CN$$ . Let $$R$$ and $$r$$ denote the circumradius and the inradius of the $$\triangle ABC$$, respectively. $$R=16$$ and $$r=6$$

Find $$\dfrac{MN}{BC}$$.

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