Question 176
$ABCD$ is a cyclic quadrilateral with $BC = CD$. The diagonals $AC$ and $BD$ intersect at $E$. Let $X$, $Y$, $Z$ and $W$ be the incentres of triangles $ riangle ABE$, $ riangle ADE$, $ riangle ABC$ and $ riangle ADC$ respectively. Show that $X$, $Y$, $Z$ and $W$ are concyclic if and only if $AB = AD$.