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Cirumradii of triangle and triangle formed by its medians

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October 9, 2010
geometrycircumcircleinequalitiesinequalities unsolved

Problem Statement

With the medians of an acute-angled triangle another triangle is constructed. If RR and RmR_m are the radii of the circles circumscribed about the first and the second triangle, respectively, prove that Rm>56RR_m>\frac{5}{6}R