« Vrati se
Given a cyclic quadrilateral ABCD, let M be the midpoint of the side CD, and let N be a point on the circumcircle of triangle ABM. Assume that the point N is different from the point M and satisfies \frac{AN}{BN}=\frac{AM}{BM}. Prove that the points E, F, N are collinear, where E=AC\cap BD and F=BC\cap DA.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
2256IMO Shortlist 2007 problem G85
2223IMO Shortlist 2006 problem G75
2176IMO Shortlist 2004 problem N70
2168IMO Shortlist 2004 problem G75
2138IMO Shortlist 2003 problem G70
2112IMO Shortlist 2002 problem G713