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Geometric angle inequality

Source: Serbia TST 2009

April 17, 2009
inequalitiestrigonometrycalculusderivativegeometryangle bisectorgeometry unsolved

Problem Statement

Let α \alpha and β \beta be the angles of a non-isosceles triangle ABC ABC at points A A and B B, respectively. Let the bisectors of these angles intersect opposing sides of the triangle in D D and E E, respectively. Prove that the acute angle between the lines DE DE and AB AB isn't greater than \frac{|\alpha\minus{}\beta|}3.
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