Distance Between Perpendicular Feet

Geometry Level 4

\(ABCD\) is a parallelogram with side lengths \(AB=338, BC=260 \) and diagonal \(AC=338\). Let \(E\) be the foot of the perpendicular from \(A\) to \(BC\), let \(F\) be the foot of the perpendicular from \(A\) to \(CD\). What is the value of \(EF\)?

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