Geometry · Regular hexagon · Rotational symmetry · Angle chasing · Concyclic points · Inscribed angle theorem
Let \(ABCDEF\) be a regular hexagon. A point \(M\) is taken on the diagonal \(AC\) and a point \(N\) on the diagonal \(CE\) so that both are placed at the same relative position:
\[ \frac{AM}{AC} = \frac{CN}{CE} = \lambda . \]
Determine \(\lambda\), given that the points \(B\), \(M\), \(N\) lie on one line.
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Serbian National Competition (Drzavno takmicenje) 2007, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source