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Show 4 points are concyclic

Source: 2022 Nigerian Senior MO Round 2/Problem 2

May 6, 2022
geometryConcycliccyclic quadrilateral

Problem Statement

Let GG be the centroid of △ABC\triangle ABC and let D,ED, E and FF be the midpoints of the line segments BC,CABC, CA and ABAB respectively. Suppose the circumcircle of △ABC\triangle ABC meets ADAD again at XX, the circumcircle of △DEF\triangle DEF meets BEBE again at YY and the circumcircle of △DEF\triangle DEF meets CFCF again at ZZ. Show that G,X,YG, X, Y and ZZ are concyclic.
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