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locus of centers of rectangles inscribed in acute triangle

Source: 2008 Cuba MO 2.8

August 27, 2024
geometryrectangleLocus

Problem Statement

Let ABCABC an acute-angle triangle. Let RR be a rectangle with vertices in the edges of ABCABC. Let OO be the center of RR. a) Find the locus of all the points OO. b) Decide if there is a point that is the center of three of these rectangles.
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