PL-OM 1994 Problem 5

A parallelopiped has vertices $A_1, A_2, ... , A_8$ and center $O$ . Show that: $4 \sum_{i=1}^8 OA_i ^2 \leq \left(\sum_{i=1}^8 OA_i \right) ^2$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.