IMO Shortlist 2006 problem G9
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Avg: 9,0 Points , , are chosen on the sides , , of a triangle respectively. The circumcircles of triangles , , intersect the circumcircle of triangle again at points , , respectively (). Points , , are symmetric to , , with respect to the midpoints of the sides , , respectively. Prove that the triangles and are similar.
Izvor: Međunarodna matematička olimpijada, shortlist 2006