# 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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