Question 117
Let $A$, $B$, $C$ and $D$ four dots on a circle in this order. Let $U$ be the intersection point of the lines $(AB)$ and $(CD)$, and $V$ the right intersection point $(BC)$ and $(DA)$. Let $K$ be the intersection point of the bisector from $U$ in the triangle $AUC$ and the bisector from $V$ in triangle $AVC$. Let $L$ be the point of intersection of the segment mediator $[KU]$ and the segment mediator $[KV]$. Show that points $U$, $V$ and $L$ are aligned. 