MathDB

Problem 2

Part of 2022 Nigerian Senior MO Round 2

Problems(1)

Show 4 points are concyclic

Source: 2022 Nigerian Senior MO Round 2/Problem 2

5/6/2022
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.
geometryConcycliccyclic quadrilateral