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In Figure, \(X\) and \(Y\) are respectively the mid-points of the opposite sides \(AD\) and \(BC\) of a parallelogram \(ABCD\). Also, \(BX\) and \(DY\) intersect \(AC\) at \(P\) and \(Q\), respectively. Show that \(AP = PQ = QC\).
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