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Line segment passing through intersection of diagonals.

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December 7, 2010
geometry unsolvedgeometry

Problem Statement

Let ABCDABCD be a convex quadrilateral whose diagonals ACAC and BDBD intersect at point OO. Let a line through OO intersect segment ABAB at MM and segment CDCD at NN. Prove that the segment MNMN is not longer than at least one of the segments ACAC and BDBD.
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