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criterion with concurrency of altitudes => circumscribed tetrahedron is regular

Source: All Russian MO 1994 ARO

July 29, 2018
geometry3D geometrytetrahedronspherealtitudes

Problem Statement

The altitudes AA1,BB1,CC1,DD1AA_1,BB_1,CC_1,DD_1 of a tetrahedron ABCDABCD intersect in the center HH of the sphere inscribed in the tetrahedron A1B1C1D1A_1B_1C_1D_1. Prove that the tetrahedron ABCDABCD is regular.
(D. Tereshin)
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