MathDB
Tetrahedron

Source: RMO 2003, Grade 8, Problem 4

October 23, 2008
geometry3D geometrytetrahedron

Problem Statement

In tetrahedron ABCD ABCD, G1,G2 G_1,G_2 and G3 G_3 are barycenters of the faces ACD,ABD ACD,ABD and BCD BCD respectively. (a) Prove that the straight lines BG1,CG2 BG_1,CG_2 and AG3 AG_3 are concurrent. (b) Knowing that AG_3\equal{}8,BG_1\equal{}12 and CG_2\equal{}20 compute the maximum possible value of the volume of ABCD ABCD.
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