Question 47
Let $ABC$ be an acute triangle. The bisector of the side $AB$ intersects the lines $BC$ and $CA$ at the points $X$ and $Y$, respectively, and the bisector of the side $AC$ intersects the lines $BC$ and $AB$ at the points $Z$ and $W$, respectively. Prove that the points $X, Y, Z$ and $W$ are concyclic.
