Inequality in a tetrahedron
Source: Moldova NMO 2002 grade 11 problem nr.8
November 3, 2008
inequalitiesgeometry3D geometrytetrahedroncircumcircle
Problem Statement
The circumradius of a tetrahedron is , and the lenghts of the segments connecting the vertices with the centroids of the opposite faces are equal to and , respectively. Prove that:
m_a\plus{}m_b\plus{}m_c\plus{}m_d\leq \dfrac{16}{3}R