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Sides of a quadrilateral in arithmetic progression

Source: Baltic Way 2010

November 19, 2010
arithmetic sequencegeometry proposedgeometry

Problem Statement

Let ABCDABCD be a convex quadrilateral with precisely one pair of parallel sides. (a)(a) Show that the lengths of its sides AB,BC,CD,DAAB,BC,CD, DA (in this order) do not form an arithmetic progression. (b)(b) Show that there is such a quadrilateral for which the lengths of its sides AB,BC,CD,DAAB ,BC,CD,DA form an arithmetic progression after the order of the lengths is changed.
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