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show that 4 faces of tetrahedron have equal area

Source: Mexican Mathematical Olympiad 1992 OMM P1

July 29, 2018
geometry3-Dimensional Geometrytetrahedron

Problem Statement

The tetrahedron OPQROPQR has the ∠POQ=∠POR=∠QOR=90o\angle POQ = \angle POR = \angle QOR = 90^o. X,Y,ZX, Y, Z are the midpoints of PQ,QRPQ, QR and RP.RP. Show that the four faces of the tetrahedron OXYZOXYZ have equal area.
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