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2016 JBMO TST- Macedonia, problem 2

Source: 2016 JBMO TST- Macedonia

May 27, 2019
2016JMMOMacedoniaJuniorgeometryparallelogram

Problem Statement

Let ABCDABCD be a parallelogram and let EE, FF, GG, and HH be the midpoints of sides ABAB, BCBC, CDCD, and DADA, respectively. If BH∩AC=IBH \cap AC = I, BD∩EC=JBD \cap EC = J, AC∩DF=KAC \cap DF = K, and AG∩BD=LAG \cap BD = L, prove that the quadrilateral IJKLIJKL is a parallelogram.
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