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unit square covered with 3 equal disks with radius <= 1/sqrt2

Source: 1983 Swedish Mathematical Competition p5

March 28, 2021
geometrycombinatorial geometrycombinatoricsdisksdiscsGeometric Inequalitiesmin

Problem Statement

Show that a unit square can be covered with three equal disks with radius less than 12\frac{1}{\sqrt{2}}. What is the smallest possible radius?
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