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ASU 438 All Soviet Union MO 1986 triangle, square around unit circle, areas

Source:

August 7, 2019
areascirclesquaregeometrygeometric inequality

Problem Statement

A triangle and a square are circumscribed around the unit circle. Prove that the intersection area is more than 3.43.4. Is it possible to assert that it is more than 3.53.5?
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