Locus of centers of rectangles
Source: Italian TST day 1, n°1
June 1, 2007
geometryrectangleincentergeometric transformationhomothetyreflectiongeometry proposed
Problem Statement
Let an acute triangle.
(a) Find the locus of points that are centers of rectangles whose vertices lie on the sides of ;
(b) Determine if exist some points that are centers of distinct rectangles whose vertices lie on the sides of .