# Equiangular Hexagon

Geometry Level 5

Equiangular hexagon $$ABCDEF$$ has $$AB=BC=DE=EF=4$$ and $$AF=CD=1$$. The hexagon is reflected across the segment $$EF$$ to form hexagon $$A'B'C'D'EF$$. $$\overline{B'C}$$ intersects $$\overline{EF}$$ at point $$P$$. $$\dfrac{EP}{FP}$$ can be expressed as $$\dfrac{p}{q}$$ for relatively prime positive integers $$p,q$$. Find $$p\times q$$.

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