IMO Shortlist 1987 problem 4


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2. travnja 2012.
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Let ABCDEFGH be a parallelepiped with AE \parallel BF \parallel CG \parallel DH. Prove the inequality
AF + AH + AC \leq  AB + AD + AE + AG.
In what cases does equality hold?

Proposed by France.
Izvor: Međunarodna matematička olimpijada, shortlist 1987