IMO 1983 LL LUX43

Given a square ABCD, let P, Q, R, and S be four variable

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IMO 1983 LL LUX43

Origin: LUX

Problem

Given a square ABCD, let P, Q, R, and S be four variable points on the sides AB, BC, CD, and DA, respectively. Determine the positions of the points P, Q, R, and S for which the quadrilateral PQRS is a parallelogram, a rectangle, a square, or a trapezoid.