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Cyclic quadrilateral geometry in the style of V. Thebault

Source: IMO Shortlist 2004 geometry problem G8

May 27, 2005
geometrycircumcircleIMO Shortlistprojective geometryPolarsBrocardpower of a point

Problem Statement

Given a cyclic quadrilateral ABCDABCD, let MM be the midpoint of the side CDCD, and let NN be a point on the circumcircle of triangle ABMABM. Assume that the point NN is different from the point MM and satisfies ANBN=AMBM\frac{AN}{BN}=\frac{AM}{BM}. Prove that the points EE, FF, NN are collinear, where E=AC∩BDE=AC\cap BD and F=BC∩DAF=BC\cap DA.
Proposed by Dusan Dukic, Serbia and Montenegro
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