Parallel Tangent

Geometry Level 2

In \(\triangle ABC,\) \(AB=6 \) , \(BC = 4\) and \( AC=8.\) A segment parallel to \( \overline{BC}\) and tangent to the incircle of \(\triangle ABC\) intersects \(\overline{AB}\) at \(M\) and \(\overline{AC}\) at \(N\).

If \(MN=\dfrac{a}{b}\), where \(a\) and \(b\) are co-prime positive integers, what is the value of \(a+b\) ?

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