IMO Shortlist 1997 problem 9

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Dodao/la: arhiva
2. travnja 2012.
Let A_1A_2A_3 be a non-isosceles triangle with incenter I. Let C_i, i = 1, 2, 3, be the smaller circle through I tangent to A_iA_{i+1} and A_iA_{i+2} (the addition of indices being mod 3). Let B_i, i = 1, 2, 3, be the second point of intersection of C_{i+1} and C_{i+2}. Prove that the circumcentres of the triangles A_1 B_1I,A_2B_2I,A_3B_3I are collinear.
Izvor: Međunarodna matematička olimpijada, shortlist 1997