« Vrati se
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.

Slični zadaci

2028IMO Shortlist 1999 problem G55
2168IMO Shortlist 2004 problem G75
2169IMO Shortlist 2004 problem G813
2176IMO Shortlist 2004 problem N70
2223IMO Shortlist 2006 problem G75
2256IMO Shortlist 2007 problem G85