MathDB
czech republic,czech and slovakia MO(third round),2008 p6

Source:

February 25, 2012
inequalitiesinequalities proposedgeometric inequalityTrianglemedian

Problem Statement

Find the greatest value of pp and the smallest value of qq such that for any triangle in the plane, the inequality p<a+mb+n<qp<\frac{a+m}{b+n}<q holds, where a,ba,b are it's two sides and m,nm,n their corresponding medians.
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