IL-GILLIS 2017 Problem 1

[list=a] [] In the right picture there is a square with four congruent circles inside it. Each circle is tangent to two others, and to two of the edges of the square. Evaluate the ratio between the blue part and white part of the square's area. [] In the left picture there is a regular hexagon with six congruent circles inside it. Each circle is tangent to two others, and to one of the edges on the hexagon in its midpoint. Evaluate the ratio between the blue part and white part of the hexagon's area. [/list]