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Geometric ineq. (IMO SL 1987-P4)

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August 19, 2010
geometrygeometric inequality3D geometrypolyhedronIMO Shortlist

Problem Statement

Let ABCDEFGHABCDEFGH be a parallelepiped with AE∥BF∥CG∥DHAE \parallel BF \parallel CG \parallel DH. Prove the inequality AF+AH+AC≤AB+AD+AE+AG.AF + AH + AC \leq AB + AD + AE + AG. In what cases does equality hold?
Proposed by France.
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