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In plane geometry, Holditch's theorem states that if a chord of fixed length is allowed to rotate inside a convex closed curve, then the locus of a point on the chord a distance p from one end and a distance q from the other is a closed curve whose area is less than that of the original curve by Πpq. In this article we obtain, first, sufficient conditions to ensure the existence of the Holditch curve and, second, a version of Holditch's theorem for convex polygons where the ellipse involved is explicitly shown. [ABSTRACT FROM AUTHOR]