In the [ABCD] tetrahedron having all the faces acute angled triangles, is denoted by rX, RX the radius lengths of the circle inscribed and circumscribed respectively on the face opposite to the X∈{A,B,C,D} peak, and with R the length of the radius of the sphere circumscribed to the tetrahedron. Show that inequality occurs8R2≥(rA+RA)2+(rB+RB)2+(rC+RC)2+(rD+RD)2 tetrahedroncircumsphereinsphere3D geometryinequalitiesexsphere