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Four circles of unit radius are arranged so that they are tangent, and their centers form a square.  A large circle is drawn, containing the four circles.  What is the radius of the large circle?

 

 May 5, 2020
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The centers of the four smaller circles are the vertices of a square.

The distance from one vertex to its adjacent vertex is 2.

This means that the distance across the square is 2·sqrt(2).

This makes the diameter of the circle 2 + 2·sqrt(2) and its radius 1 + sqrt(2).

 May 6, 2020

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