Distance between midpoints independent of reflection lines
Source: Czech-Polish-Slovak Match, 2009
August 20, 2011
geometrygeometric transformationreflectionparallelogramgeometry unsolved
Problem Statement
Given a circle, let be a chord that is not a diameter, and let be a point on the longer arc . Let and denote the reflections of and , respectively, about lines and , respectively. Prove that the distance between the midpoint of and the midpoint of is independent of the choice of .