# What name shall I give to this problem? - 2

Geometry Level 5

In $$\triangle ABC$$, $$D$$ and $$E$$ are points on $$BC$$ such that $$BD = DE = EC$$. $$F$$ is a point on $$AC$$ such that $$AF=FC$$. If $$AD$$ and $$AE$$ intersect $$BF$$ respectively at $$P$$ and $$Q$$. Then, the ratio $$\dfrac{BP}{PQ}$$ can be expressed as $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are coprime integers. Find $$10a+b$$.

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