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concyclic projections and a point symmetry lead also to concyclic projections

Source: Sharygin 2006 finals 10.2

September 29, 2019
symmetryConcyclicprojectionsgeometry

Problem Statement

The projections of the point XX onto the sides of the ABCDABCD quadrangle lie on the same circle. YY is a point symmetric to XX with respect to the center of this circle. Prove that the projections of the point BB onto the lines AX,XC,CY,YAAX,XC, CY, YA also lie on the same circle.
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