« Vrati se
Let ABC be a triangle, \Omega its incircle and \Omega_{a}, \Omega_{b}, \Omega_{c} three circles orthogonal to \Omega passing through (B,C),(A,C) and (A,B) respectively. The circles \Omega_{a} and \Omega_{b} meet again in C'; in the same way we obtain the points B' and A'. Prove that the radius of the circumcircle of A'B'C' is half the radius of \Omega.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
2253IMO Shortlist 2007 problem G52
2195IMO Shortlist 2005 problem G612
2194IMO Shortlist 2005 problem G515
2136IMO Shortlist 2003 problem G511
2031IMO Shortlist 1999 problem G83
2027IMO Shortlist 1999 problem G40