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Axis of median

Source: Czech and Slovak Olympiad 2015, National Round, Problem 3

April 1, 2015
geometry

Problem Statement

In triangle △ABC\triangle ABC with median from BB not perpendicular to ABAB nor BCBC, we call XX and YY points on ABAB and BCBC, which lie on the axis of the median from BB. Find all such triangles, for which A,C,X,YA,C,X,Y lie on one circumrefference.
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