International Mathematical Olympiad 2002 Problem 2

$BC$ is a diameter of a circle center $O$. $A$ is any point on the circle with $\angle AOC>60^{\circ}$. $EF$ is the chord which is the perpendicular bisector of $AO$. $D$ is the midpoint of the minor arc $AB$. The line through $O$ parallel to $AD$ meets $AC$ at $J$. Show that $J$ is the incenter of triangle $CEF$.