Equiangular Hexagon

Geometry Level 5

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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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