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Trapezoid and squares

Source: First Romanian JBMO TST 2023 P5

April 14, 2023
geometry

Problem Statement

Outside of the trapezoid ABCDABCD with the smaller base ABAB are constructed the squares ADEFADEF and BCGHBCGH. Prove that the perpendicular bisector of ABAB passes through the midpoint of FHFH.
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