MathDB
6 midpoints are coplanar, given 3 parallelograms in space

Source: Israel Grosman Memorial Mathematical Olympiad 1999 p6

February 15, 2020
geometryparallelogram3D geometrycoplanarmidpoints

Problem Statement

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