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A convex quadrilateral $A B C D$ is inscribed in the circle with diameter $A B$. Let $A B$ and $C D$ meet at $I, A D$ and $B C$ at $J$, and $A C$ and $B D$ at $K$, and let $N$ be a point on $A B$. Prove that $I K \perp J N$ if and only if $N$ is the midpoint of $A B$.
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