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Any three points contained in equilateral triangle

Source: China TST 2021, Test 2, Day 2 P6

March 22, 2021
geometry

Problem Statement

Find the smallest positive real constant aa, such that for any three points A,B,CA,B,C on the unit circle, there exists an equilateral triangle PQRPQR with side length aa such that all of A,B,CA,B,C lie on the interior or boundary of △PQR\triangle PQR.
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