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min radius such 3 equal circles cover a square

Source: Czech-Polish-Slovak Junior Match 2013, Team p6 CPSJ

March 21, 2020
geometrycirclesequal circlessquare

Problem Statement

There is a square ABCDABCD in the plane with ∣AB∣=a|AB|=a. Determine the smallest possible radius value of three equal circles to cover a given square.
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