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2AD <BE + EA for angle bisectors in an isosceles 100-40-40 triangle

Source: Moldova JBMO TST 2000 1.3

July 9, 2020
geometryangle bisectorgeometric inequalityisosceles

Problem Statement

Let ABCABC be a triangle with AB=ACAB = AC ¸ ∠BAC=100o\angle BAC = 100^o and AD,BEAD, BE angle bisectors. Prove that 2AD<BE+EA2AD <BE + EA
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