Question 102
In scalene triangle $ABC$, the incenter is $I$ and the circumcenter is $O$. $AI$ intersects the circumcircle of $ABC$ a second time at $P$. The line passing through $I$ and perpendicular to $AI$ intersects $BC$ at $X$. The foot of the perpendicular from $X$ to $IO$ is $Y$. Show that the points $A$, $P$, $X$, $Y$ are concyclic.