Circumradius and Inradius

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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