Τετάρτη, 11 Οκτωβρίου 2017

2000 JBMO Shortlist 20

Let ${ABC}$ be a triangle and let ${a, b, c}$ be the lengths of the sides ${BC,CA,AB}$ respectively. Consider a triangle ${DEF}$ with the side lengths ${EF = \sqrt{au}, FD = \sqrt{bu}, DE = \sqrt{cu}}$. Prove that ${\angle A >\angle B > \angle C}$ implies ${\angle A > \angle D > \angle E > \angle F > \angle C}$.

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