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Consider a triangle ABC with AB=13, BC=1...

Consider a triangle ABC with AB=13, BC=14, CA=15. A line perpendicular to BC divides the interior of `DeltaABC` into two regions of equal area. Suppose that the aforesaid perpendicular cuts BC at D, and cuts `DeltaABC` again at E. If L is the length of the line segment DE, find `L^(2)`.

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