Toufik Mansour and Mark Shattuck, On a certain cubic geometric inequality,
Forum Geometricorum, 11 (2011) 175--181.

Abstract.   We provide a proof of a geometric inequality relating the cube of the distances of an arbitrary point from the vertices of a triangle to the cube of the inradius of the triangle. Comparable versions of the inequality involving second and fourth powers may be obtained by modifying our arguments.

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