« Vrati se
Points A_{1}, B_{1}, C_{1} are chosen on the sides BC, CA, AB of a triangle ABC respectively. The circumcircles of triangles AB_{1}C_{1}, BC_{1}A_{1}, CA_{1}B_{1} intersect the circumcircle of triangle ABC again at points A_{2}, B_{2}, C_{2} respectively (A_{2}\neq A, B_{2}\neq B, C_{2}\neq C). Points A_{3}, B_{3}, C_{3} are symmetric to A_{1}, B_{1}, C_{1} with respect to the midpoints of the sides BC, CA, AB respectively. Prove that the triangles A_{2}B_{2}C_{2} and A_{3}B_{3}C_{3} are similar.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
2138IMO Shortlist 2003 problem G70
2168IMO Shortlist 2004 problem G75
2169IMO Shortlist 2004 problem G815
2176IMO Shortlist 2004 problem N70
2223IMO Shortlist 2006 problem G75
2256IMO Shortlist 2007 problem G85