Question 45
In a triangle $ABC$, let $D$ and $E$ be the feet of the angle bisectors of angles $A$ and $B$, respectively. A rhombus is inscribed into the quadrilateral $AEDB$ (all vertices of the rhombus lie on different sides of $AEDB$). Let $\phi$ be the non-obtuse angle of the rhombus. Prove that $\phi \le \max\{\angle BAC, \angle ABC\}$.