# RMO is really insane

Geometry Level 3

Let $$ABC$$ be a triangle.Let $$D$$ and $$C$$ be points on segments $$BC$$ 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 area of the triangle $$APQ$$ to that of the quadrilateral $$PDEQ$$.

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