Question 113
Let $ABC$ be a triangle with $\widehat{BAC}=60^{\circ}$. Let $D$ and $E$ be the feet of the bisectors from the vertices $B$ and $C$ respectively. Let $I$ be the intersection point of the line $(BD)$ and $(CE)$. Show that points $A$, $I$, $D$ and $E$ are cocyclic.