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ABC is an acute-angled triangle with area 1

Source: Balkan MO 1999, Problem 3

April 24, 2006
geometryinequalitiestrigonometryfunctiongeometry proposed

Problem Statement

Let ABCABC be an acute-angled triangle of area 1. Show that the triangle whose vertices are the feet of the perpendiculars from the centroid GG to ABAB, BCBC, CACA has area between 427\frac 4{27} and 14\frac 14.
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