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MMO 301 Moscow MO 1955 <OAB, <OBA, <OBC, <OCB,<OAC,<OCA acute, trihedral

Source:

August 17, 2019
trihedral angleanglesacute3D geometrygeometry

Problem Statement

Given a trihedral angle with vertex OO. Find whether there is a planar section ABCABC such that the angles ∠OAB\angle OAB, ∠OBA\angle OBA, ∠OBC\angle OBC, ∠OCB\angle OCB, ∠OAC\angle OAC, ∠OCA\angle OCA are acute.
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