Question 55
$ABCD$ is a parallelogram. The excircle of $ABC$ opposite $A$ has center $E$ and touches the line $AB$ at $X$. The excircle of $ADC$ opposite $A$ has center $F$ and touches the line $AD$ at $Y$. The line $FC$ meets the line $AB$ at $W$, and the line $EC$ meets the line $AD$ at $Z$. Show that $WX = YZ$.