IMO Shortlist 1991 problem 6


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ABCD is a terahedron: AD+BD=AC+BC, BD+CD=BA+CA, CD+AD=CB+AB, M,N,P are the mid points of BC,CA,AB. OA=OB=OC=OD. Prove that \angle MOP = \angle NOP =\angle NOM.
Izvor: Međunarodna matematička olimpijada, shortlist 1991