# Not For Those Who Are Slaves of Trigonometry

Geometry Level 4

In the diagram, triangle $$ABC$$ with the incircle touches $$AB$$ and $$BC$$ at $$F$$ and $$E$$, respectively.

$$M$$ and $$N$$ are midpoints of $$AC$$ and $$BC$$, respectively.

$$EF$$ cuts $$MN$$ at point $$P$$. $$AP$$ cuts $$BC$$ at point $$D$$.

If $$AB=4, AC=5$$ and $$BC=6$$, length of $$AD$$ can be written as $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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