MathDB

2

Part of 2016 Macedonia JBMO TST

Problems(1)

2016 JBMO TST- Macedonia, problem 2

Source: 2016 JBMO TST- Macedonia

5/27/2019
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.
2016JMMOMacedoniaJuniorgeometryparallelogram