Geometry · Angle chasing · Isosceles triangles · Auxiliary construction · Equilateral triangle · Cyclic quadrilateral · Circumcentre
In a triangle \(ABC\) the angle at \(B\) equals \(80^\circ\). Three further points are marked:
the point \(D\) on the side \(BC\) with \(AB = AD = CD\); the point \(F\) on the side \(AB\) with \(AF = BD\); and the point \(E\) on the line \(BC\), placed so that \(C\) lies between \(B\) and \(E\), with \(\angle BEF = 20^\circ\).
Prove that \(DE = AC\).
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Serbian National Competition (Drzavno takmicenje) 2010, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source