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min c such that S(MKNL)<c S(ABCD)

Source: Belarus TST 2009 5.1

June 13, 2020
geometrygeometric inequalityareasareamidpoints

Problem Statement

Let M,NM,N be the midpoints of the sides AD,BCAD,BC respectively of the convex quadrilateral ABCDABCD, K=AN∩BMK=AN \cap BM, L=CM∩DNL=CM \cap DN. Find the smallest possible c∈Rc\in R such that S(MKNL)<c⋅S(ABCD)S(MKNL)<c \cdot S(ABCD) for any convex quadrilateral ABCDABCD.
I. Voronovich
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