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?

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).