IMO Shortlist 1999 problem G8

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Dodao/la: arhiva
2. travnja 2012.
Given a triangle ABC. The points A, B, C divide the circumcircle \Omega of the triangle ABC into three arcs BC, CA, AB. Let X be a variable point on the arc AB, and let O_{1} and O_{2} be the incenters of the triangles CAX and CBX. Prove that the circumcircle of the triangle XO_{1}O_{2} intersects the circle \Omega in a fixed point.
Izvor: Međunarodna matematička olimpijada, shortlist 1999