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equal products of areas in convex hecagon with concurrent diagonals

Source: Norwegian Mathematical Olympiad 2011 - Abel Competition p2b

September 4, 2019
geometryhexagondiagonalsconcurrencyconcurrentarea of a triangleareas

Problem Statement

The diagonals AD,BEAD, BE, and CFCF of a convex hexagon ABCDEFABCDEF intersect in a common point. Show that a(ABE)a(CDA)a(EFC)=a(BCE)a(DEA)a(FAC)a(ABE) a(CDA) a(EFC) = a(BCE) a(DEA) a(FAC), where a(KLM)a(KLM) is the area of the triangle KLMKLM. https://cdn.artofproblemsolving.com/attachments/0/a/bcbbddedde159150fe3c26b1f0a2bfc322aa1a.png