# RMO ( 2016 ) Triangle Vs Quadrilateral

Geometry Level 5

Let $$ABC$$ be a triangle. Let $$D, E$$ be a points on the segment $$BC$$ such that $$BD = DE = EC$$. Let $$F$$ be the midpoint of $$AC$$. Let $$BF$$ intersect $$AD$$ in $$P$$ and $$AE$$ in $$Q$$, respectively.

Determine the ratio of the area of the triangle $$APQ$$ to that of the quadrilateral $$PDEQ$$.

If this ratio can be expressed as $$\dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers, submit your answer as $$p + q$$.

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