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segment bisect area of convex quadrilateral , parallel wanted

Source: 2004 Estonia National Olympiad Final Round grade 9 p3

March 25, 2020
geometrybisects areaconvexparallel

Problem Statement

On the sides AB,BCAB , BC of the convex quadrilateral ABCDABCD lie points MM and NN such that ANAN and CMCM each divide the quadrilateral ABCDABCD into two equal area parts. Prove that the line MNMN and ACAC are parallel.
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