Five circles in a square - adapted from Polya
In a green square of side A there a five non-overlapping blue circles. One of the circles has radius R, is concentric with the square and is tangent to the other four circles. Each of the other circles has radius r and is tangent to two sides of the square. For a fixed value of A, write R as a function of r. What fraction of the area of the square is covered by the circles?