\( P, Q, R \) and \( S \) are respectively the mid-points of the sides \( A B, B C, C D \) and \...

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\( P, Q, R \) and \( S \) are respectively the mid-points of the sides \( A B, B C, C D \) and \( D A \) of a quadrilateral \( A B C D \), such that \( A C \perp B D \). Prove that \( P Q R S \) is a rectangle.
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