MathDB

6

Part of 1988 ITAMO

Problems(1)

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

Source: ITAMO 1988 p6

2/2/2020
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.
3D geometrygeometrytetrahedrongeometric inequality