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Inequality of angles - JBMO Shortlist

Source:

October 30, 2010
inequalitiesgeometry proposedgeometrygeometry unsolved

Problem Statement

Let ABCABC be a triangle and let a,b,ca,b,c be the lengths of the sides BC,CA,ABBC, CA, AB respectively. Consider a triangle DEFDEF with the side lengths EF=auEF=\sqrt{au}, FD=buFD=\sqrt{bu}, DE=cuDE=\sqrt{cu}. Prove that ∠A>∠B>∠C\angle A >\angle B >\angle C implies ∠A>∠D>∠E>∠F>∠C\angle A >\angle D >\angle E >\angle F >\angle C.
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