Geometry · Angle chasing · Equilateral triangle · Cevians · 30 60 90 triangle · Thales circle
In triangle \(ABC\) the sides satisfy \(|AB| = 2|AC|\). A point \(D\) is chosen on side \(AB\) and a point \(E\) on side \(BC\) so that \(\angle BAE = \angle ACD\). The segments \(AE\) and \(CD\) intersect at \(F\), and the triangle \(CFE\) is equilateral. Determine the angles of triangle \(ABC\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2009, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source