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Segments bisect the area of quadrilateral.

Source: 40th Canadian Mathematical Olympiad (2008 #1)

April 21, 2008
geometryratiogeometry proposed

Problem Statement

ABCD ABCD is a convex quadrilateral for which AB AB is the longest side. Points M M and N N are located on sides AB AB and BC BC respectively, so that each of the segments AN AN and CM CM divides the quadrilateral into two parts of equal area. Prove that the segment MN MN bisects the diagonal BD BD.
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