Geometry · Square · Congruent triangles · Collinearity
Let \(ABCD\) be a square and let \(E\) be the midpoint of its side \(CD\). The line through \(D\) perpendicular to the diagonal \(BD\) meets the line \(AE\) at a point \(F\). Prove that the points \(B\), \(C\) and \(F\) are collinear.
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Serbian Municipal Competition 2012, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source