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BALTIC-WAY 2008 Problem 17

    Assume that a,b,ca, b, c and dd are the sides of a quadrilateral inscribed in a given circle. Prove that the product (ab+cd)(ac+bd)(ad+bc)(a b+c d)(a c+b d)(a d+b c) acquires its maximum when the quadrilateral is a square.

    Dataset text NuminaMath olympiads. Quoted with source.

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