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Geometry Mathley 16.1 four concurrent Euler lines

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June 14, 2020
Euler Lineconcurrentgeometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral with two diagonals intersect at EE. Let M M, NN, PP, QQ be the reflections of E E in midpoints of ABAB, BCBC, CDCD, DADA respectively. Prove that the Euler lines of △MAB \triangle MAB, △NBC\triangle NBC, △PCD,\triangle PCD, △QDA\triangle QDA are concurrent.
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