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Geometric inequality involving some bisectors

Source: Romania TST 4 2012, Problem 1

May 16, 2012
inequalitiestrigonometryfunctiontrig identitiesLaw of Cosinesinequalities proposed

Problem Statement

Let ΔABC\Delta ABC be a triangle. The internal bisectors of angles ∠CAB\angle CAB and ∠ABC\angle ABC intersect segments BCBC, respectively ACAC in DD, respectively EE. Prove that DE≤(3−22)(AB+BC+CA).DE\leq (3-2\sqrt{2})(AB+BC+CA).
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