Problem

Source: Israel Grosman Memorial Mathematical Olympiad 1999 p6

Tags: geometry, parallelogram, 3D geometry, coplanar, midpoints



Let $A,B,C,D,E,F$ be points in space such that the quadrilaterals $ABDE,BCEF, CDFA$ are parallelograms. Prove that the six midpoints of the sides $AB,BC,CD,DE,EF,FA$ are coplanar