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Let ABC be an acute triangle...

Source: Bulgarian IMO TST 2005, Day 1, Problem 1

July 7, 2013
trigonometrygeometry proposedgeometry

Problem Statement

Let ABCABC be an acute triangle. Find the locus of the points MM, in the interior of △ABC\bigtriangleup ABC, such that AB−FG=MF.AG+MG.BFCMAB-FG= \frac{MF.AG+MG.BF}{CM}, where FF and GG are the feet of the perpendiculars from MM to the lines BCBC and ACAC, respectively.
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