RS-SMO 2009

In a scalene triangle $ABC$ , $\alpha$ and $\beta$ respectively denote the interior angles at vertixes $A$ and $B$ . The bisectors of these two angles meet the opposite sides of the triangle at points $D$ and $E$ , respectively. Prove that the acute angle between the lines $DE$ and $AB$ does not exceed $\frac{ | \alpha - \beta |}{3}$ . Proposed by Dusan Djukic

Find the smallest natural number which is a multiple of $2009$ and whose sum of (decimal) digits equals $2009$ Proposed by Milos Milosavljevic