Tetrahedron problem
Source: Kvant Magazine No. 5 2023 M2747 [thanks for the translation, NO_SQUARES]
January 9, 2024
geometry3D geometrytetrahedron
Problem Statement
In the tetrahedron on the continuation of the edges and , three points were marked for point located from at a distance equal to the semi-perimeter of the triangle Similarly, we marked three points corresponding to vertices and Prove that if there is a sphere touching all the edges of the tetrahedron , then the marked 12 points lie on the same sphere.Proposed by V. Alexandrov