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RU-ALLRUSSIAN 1980 Problem 4

    ABCD is a convex quadrilateral. M is the midpoint of BC and N is the midpoint of CD. If k=AM+ANk = \mathrm{AM} + \mathrm{AN} show that the area of ABCD is less than k2/2k^2 /2 .

    Dataset text NuminaMath olympiads. Quoted with source.

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