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BALTIC-WAY 2010 Problem 12

    Let ABCDA B C D be a convex quadrilateral with precisely one pair of parallel sides.

    a) Show that the lengths of its sides AB,BC,CD,DAA B, B C, C D, D A (in this order) do not form an arithmetic progression.

    b) Show that there is such a quadrilateral for which the lengths of its sides AB,BC,CDA B, B C, C D, DAD A form an arithmetic progression after the order of the lengths is changed.

    Dataset text NuminaMath olympiads. Quoted with source.

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