MathNet 2006 — Part 03 Question 164

Let $A$, $B$, $C$, $D$, $E$, $F$ be points on a circle with $A E \| B D$ and $B C \| D F$. By reflecting on the straight line $C E$, the point $D$ changes into $X$. Show that $X$ is as far from the line $E F$ as $B$ is from $A C$.