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RU-ALLRUSSIAN 1962 Problem 11

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The triangle ABC satisfies 0≤AB≤1≤BC≤2≤CA≤30\leq \mathrm{AB}\leq 1\leq \mathrm{BC}\leq 2\leq \mathrm{CA}\leq 3 . What is the maximum area it can have?

Dataset text NuminaMath olympiads. Quoted with source.

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