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locus of points C such points A,B,C can be covered by circle of radius 1

Source: Sharygin 2010 Final 8.2

October 2, 2018
geometryLocuscircle

Problem Statement

Two points AA and BB are given. Find the locus of points CC such that triangle ABCABC can be covered by a circle with radius 11.
(Arseny Akopyan)