Problem

Source: 2022 Nigerian Senior MO Round 2/Problem 2

Tags: geometry, Concyclic, cyclic quadrilateral



Let G be the centroid of ABC and let D,E and F be the midpoints of the line segments BC,CA and AB respectively. Suppose the circumcircle of ABC meets AD again at X, the circumcircle of DEF meets BE again at Y and the circumcircle of DEF meets CF again at Z. Show that G,X,Y and Z are concyclic.