Consider a parallelogram p = (KLMN) and a point J inside it. Construct the quadrangle q = (OQPR), having vertices the reflections of J on the sides of p. Show that: (a) The area of q is the same for all positions of J inside p. (b) The diagonals of q cut at J and are double the length of the distances of the parallel sides of p. (c) q is a trapezium, exactly when J is on a diagonal of p.

Look at Orthogonal_Diagonals.html , for a related subject.

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