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x+y+z <= a+b+c+3d , in a tetrahedron

Source: ITAMO 1988 p6

February 2, 2020
3D geometrygeometrytetrahedrongeometric inequality

Problem Statement

The edge lengths of the base of a tetrahedron are a,b,ca,b,c, and the lateral edge lengths are x,y,zx,y,z. If dd is the distance from the top vertex to the centroid of the base, prove that x+y+z≤a+b+c+3dx+y+z \le a+b+c+3d.
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