Question 43
The internal angle bisectors at vertices $A$ and $B$ of triangle $ABC$ meet the opposite sides at $D$ and $E$, respectively. A rhombus is inscribed in quadrilateral $ABDE$ so that exactly one vertex of the rhombus lies on each side of the quadrilateral. If $\angle BAC=\alpha$ and $\angle ABC=\beta$, prove that at least one angle of the rhombus is no greater than $\max\{\alpha, \beta\}$.
(Dušan Đukić)
(Dušan Đukić)