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2016 preRMO p5, line perpendicular to BC bisects triangle's area

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August 9, 2019
geometryareas

Problem Statement

Consider a triangle ABCABC with AB=13,BC=14,CA=15AB = 13, BC = 14, CA = 15. A line perpendicular to BCBC divides the interior of △BC\vartriangle BC into two regions of equal area. Suppose that the aforesaid perpendicular cuts BCBC at DD, and cuts △ABC\vartriangle ABC again at EE. If LL is the length of the line segment DEDE, find L2L^2.
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