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intersections of the diagonals of rectangles

Source: Canadian Mathematical Olympiad 2006, problem 2

January 28, 2007
geometryrectanglegeometry proposed

Problem Statement

Let ABCABC be acute triangle. Inscribe a rectangle DEFGDEFG in this triangle such that D∈AB,E∈AC,F∈BC,G∈BCD\in AB,E\in AC,F\in BC,G\in BC. Describe the locus of (i.e., the curve occupied by) the intersections of the diagonals of all possible rectangles DEFGDEFG.
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