Question 54
In an acute triangle $ABC$, denote the interior angles by $\alpha,\beta,\gamma$ as usual. Let $D$ be the intersection of the bisector of $\alpha$ with $BC$, and let $E$ be the intersection of the bisector of $\beta$ with $AC$. A rhombus is inscribed in quadrilateral $ABDE$, with its vertices on four different sides. Denote its non-obtuse interior angles by $\varphi$. Prove that $\varphi\le\max(\alpha,\beta)$.