Question 155
Let $ABCDEF$ be a hexagon circumscribing a circle $\omega$. The sides $AB$, $BC$, $CD$, $DE$, $EF$, $FA$ touch $\omega$ at $U$, $V$, $W$, $X$, $Y$, and $Z$ respectively; moreover, $U$, $W$, and $Y$ are the midpoints of sides $AB$, $CD$, and $EF$, respectively. Prove that $UX$, $VY$, and $WZ$ are concurrent.