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Center of gravity of a tetrahedron

Source: 2002 Austrian-Polish, problem 3

September 23, 2006
geometry3D geometrytetrahedrongeometry unsolved

Problem Statement

Let ABCDABCD be a tetrahedron and let SS be its center of gravity. A line through SS intersects the surface of ABCDABCD in the points KK and LL. Prove that 13≤KSLS≤3\frac{1}{3}\leq \frac{KS}{LS}\leq 3
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