Geometry · Cyclic polygons · Central angles · Chord midpoints · Congruent triangles · Rotations
A pentagon \(ABCDE\) is inscribed in a circle of radius \(r\), and three of its sides have length \(r\):
\[ AB = BC = DE = r . \]
Let \(G\) and \(F\) be the midpoints of the sides \(CD\) and \(EA\). Prove that the triangle \(BGF\) is equilateral.
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Serbian Republic Competition (Republicko takmicenje) 2006, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source