Geometry · Squares · Congruent triangles · Isosceles trapezoid · Parallelograms · Perpendicularity
Let \(E\) be a point on the side \(CD\) of a square \(ABCD\). The point \(F\) lies on the line \(AB\) but not on the segment \(AB\), and satisfies \(|BF| = |DE|\). Prove that the lines \(AC\) and \(EF\) are perpendicular.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2012, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source