MathDB
Conditions on sides & diagonals => ABCD is a parallelogram

Source: Czech-Polish-Slovak Match, 2010

August 8, 2011
geometryparallelogramgeometric transformationreflectioninequalitiestriangle inequalitygeometry unsolved

Problem Statement

Let ABCDABCD be a convex quadrilateral for which AB+CD=2⋅ACandBC+DA=2⋅BD. AB+CD=\sqrt{2}\cdot AC\qquad\text{and}\qquad BC+DA=\sqrt{2}\cdot BD. Prove that ABCDABCD is a parallelogram.
Back to ProblemsView on AoPS