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tetrahedron

Source: IMO ShortList 1991, Problem 7 (CHN 2)

December 24, 2004
geometry3D geometrytetrahedronrhombusIMO Shortlist

Problem Statement

ABCD ABCD is a terahedron: AD\plus{}BD\equal{}AC\plus{}BC, BD\plus{}CD\equal{}BA\plus{}CA, CD\plus{}AD\equal{}CB\plus{}AB, M,N,P M,N,P are the mid points of BC,CA,AB. BC,CA,AB. OA\equal{}OB\equal{}OC\equal{}OD. Prove that \angle MOP \equal{} \angle NOP \equal{}\angle NOM.
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