MathDB
Centroid geo

Source: Baltic Way 2023/14

November 11, 2023
geometry

Problem Statement

Let ABCABC be a triangle with centroid GG. Let D,E,FD, E, F be the circumcenters of triangles BCG,CAG,ABGBCG, CAG, ABG. Let XX be the intersection of the perpendiculars from EE to ABAB and from FF to ACAC. Prove that DXDX bisects EFEF.
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