olymmath

HMMT 2004 U24

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We say a point is contained in a square if it is in its interior or on its boundary. Three unit squares are given in the plane such that there is a point contained in all three. Furthermore, three points A,B,CA, B, C, are given, each contained in at least one of the squares. Find the maximum area of triangle ABCA B C.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3 \sqrt{3}}{2}

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