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RU-ALLRUSSIAN 1967 Problem 9

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ABCD is a unit square. One vertex of a rhombus lies on side AB, another on side BC, and a third on side AD. Find the area of the set of all possible locations for the fourth vertex of the rhombus.

Dataset text NuminaMath olympiads. Quoted with source.

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2 \frac{1}{3}

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