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equal faces of perpendicular edges in tetrahedron, concurrency related

Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p6

April 18, 2022
geometry3D geometrytetrahedronconcurrency

Problem Statement

In a tetrahedron, segments connecting the midpoints of heights with the orthocenters of the faces to which these heights are drawn intersect at one point. Prove that in such a tetrahedron all faces are equal or there are perpendicular edges.
(Yu. Blinkov)