Question 98
Let $ABC$ a triangle. We denote by $D$ the foot of the bisector of $\widehat{BAC}$, and by $E$ the foot of the height from $A$. the mediator of $[AD]$ Meets the half circles of respective diameters $[AB]$ and $[AC]$ built externally at $ABC$, in $X$ and $Y$. Prove that the points $X, Y, D, E$ are cocyclic.