OBM 2000 Problem 1

A rectangular piece of paper has top edge $AD$ . A line $L$ from $A$ to the bottom edge makes an angle $x$ with the line $AD$ . We want to trisect $x$ . We take $B$ and $C$ on the vertical ege through $A$ such that $AB = BC$ . We then fold the paper so that $C$ goes to a point $C'$ on the line $L$ and $A$ goes to a point $A'$ on the horizontal line through $B$ . The fold takes $B$ to $B'$ . Show that $AA'$ and $AB'$ are the required trisectors.