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Let $P$ and $Q$ be points on a circle $k$. A chord $A C$ of $k$ passes through the midpoint $M$ of $P Q$. Consider a trapezoid $A B C D$ inscribed in $k$ with $A B \| C D$. Prove that the intersection point $X$ of $A D$ and $B C$ depends only on $k$ and $P, Q$.
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