In the tetrahedron ABCD, on the continuation of the edges AB,AC and AD, three points were marked for point A, located from A at a distance equal to the semi-perimeter of the triangle BCD. Similarly, we marked three points corresponding to vertices B,C and D. Prove that if there is a sphere touching all the edges of the tetrahedron ABCD, then the marked 12 points lie on the same sphere.Proposed by V. Alexandrov geometry3D geometrytetrahedron