IMO Shortlist 2004 problem G8


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 2004