PAMO 2004 Problem 6

Let $ABCD$ be a cyclic quadrilateral such that $AB$ is a diameter of it's circumcircle. Suppose that $AB$ and $CD$ intersect at $I$ , $AD$ and $BC$ at $J$ , $AC$ and $BD$ at $K$ , and let $N$ be a point on $AB$ . Show that $IK$ is perpendicular to $JN$ if and only if $N$ is the midpoint of $AB$ .