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concurrent circumcircles wanted 2007 Portugal p2

Source:

October 13, 2020
geometrycircumcircleconcurrentconcurrency

Problem Statement

Let [ABC][ABC] be a triangle and X,YX, Y and ZZ points on the sides [AB],[BC][AB], [BC] and [AC][AC], respectively. Prove that circumcircles of triangles AXZ,BXYAXZ, BXY and CYZCYZ intersect at a point.
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