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A trapezoid $A B C D$ with $A B \| C D$ and $A D<C D$ is inscribed in a circle $c$. Let $D P$ be a chord parallel to $A C$. The tangent to $c$ at $D$ meets the line $A B$ at $E$, and the lines $P B$ and $D C$ meet at $Q$. Prove that $E Q=A C$
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