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circumcircle of AXY passes through circumceuters of AOB and AOC

Source: 2021 Sharygin Geometry Olympiad Finals grade IX p5

August 2, 2021
ConcyclicCircumcentergeometry

Problem Statement

Let OO be the clrcumcenter of triangle ABCABC. Points XX and YY on side BCBC are such that AX=BXAX = BX and AY=CYAY = CY. Prove that the circumcircle of triangle AXYAXY passes through the circumceuters of triangles AOBAOB and AOCAOC.
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