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locus inside an equilateral triangle (2007 HOMC Senior Q8)

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July 18, 2019
geometryLocusEquilateral

Problem Statement

Let ABCABC be an equilateral triangle. For a point MM inside △ABC\vartriangle ABC, let D,E,FD,E,F be the feet of the perpendiculars from MM onto BC,CA,ABBC,CA,AB, respectively. Find the locus of all such points MM for which ∠FDE\angle FDE is a right angle.
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