Three circles and a triangle

Geometry Level 4

Three circles with equal radii are centered at (1,0),(0,0),(1,0), (0,0), and (0,1)(0,1).

To 4 decimal places, what is the smallest radius of the circles such that we can pick a point within each circle--like A, B, C in the diagram--and connect them to form an equilateral triangle?

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