Problem

Source: Sharygin 2006 finals 10.2

Tags: symmetry, Concyclic, projections, geometry



The projections of the point X onto the sides of the ABCD quadrangle lie on the same circle. Y is a point symmetric to X with respect to the center of this circle. Prove that the projections of the point B onto the lines AX,XC,CY,YA also lie on the same circle.