Plane geometry II · Chapter II · Challenge
On the sides of a triangle \(ABC\), equilateral triangles \(ADB\), \(BEC\) and \(CFA\) are constructed outwardly, so that \(D\), \(E\), \(F\) are the apexes over \(AB\), \(BC\), \(CA\) respectively. Prove that the segments \(AE\), \(BF\) and \(CD\) have equal lengths and pass through one point.
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Serbian Regional Competition (Okruzno takmicenje) 1995, high school grade I, problem 5. The 1995 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS).