MathDB

Tetrahedron

Source: All Russian Mathematical Olympiad 2008. 11.4

June 13, 2008

geometry3D geometrytetrahedronspherecircumcirclefunctionanalytic geometry

Problem Statement

Each face of a tetrahedron can be placed in a circle of radius

1

. Show that the tetrahedron can be placed in a sphere of radius

\frac{3}{2\sqrt2}