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\(O\) is the point of intersection of the diagonals \(AC\) and \(BD\) of a trapezium \(ABCD\) with \(AB||DC\). Through \(O\), a line segment \(PQ\) is drawn parallel to \(AB\) meeting \(AD\) in \(P\) and \(BC\) in \(Q\). Prove that \(PO = QO\).
 
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