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2017 Polish Junior Math Olympiad Finals P2

Source: 2017 Polish Junior Math Olympiad Finals

May 22, 2023
geometry

Problem Statement

Point DD lies on the side ABAB of triangle ABCABC, and point EE lies on the segment CDCD. Prove that if the sum of the areas of triangles ACEACE and BDEBDE is equal to half the area of triangle ABCABC, then either point DD is the midpoint of ABAB or point EE is the midpoint of CDCD.
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