Question 102
In an acute triangle $\triangle ABC$ with $|AB| \neq |AC|$, the perpendicular bisectors of sides $AC$ and $AB$ intersect segment $BC$ at points $D$ and $E$, respectively. The tangents to $\odot(ABC)$ at the points $B$ and $C$ intersect $\odot(ABD)$ and $\odot(ACE)$ at points $Y$ and $Z$, respectively. Suppose that lines $YD$ and $ZE$ intersect at point $X$. Define points $U$ and $V$ to be the intersections of $\odot(DEX)$ and the lines $AD$ and $AE$, respectively. Prove that the lines $UV, BC$ and $XA$ are concurrent.