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)