Geometry · Rhombus · Cyclic quadrilateral · Isosceles triangle · Collinearity
Let \(E\) be a point of the diagonal \(AC\) of a rhombus \(ABCD\), with \(E \ne A\) and \(E \ne C\). Let \(N\) be the point of the line \(AB\) other than \(A\) for which \(EN = EA\), and let \(M\) be the point of the line \(BC\) other than \(C\) for which \(EM = EC\). Denote by \(K\) the intersection point of the lines \(AM\) and \(CN\).
Prove that the points \(K\), \(E\) and \(D\) lie on one line.
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Serbian Municipal Competition 2004, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source