MathDB

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

Problem Statement