Regular Polygons and Circles

A.

In the right-hand figure, there is a square containing 4 circles. The radii of the circles are equal to each other, and each circle is tangent to two other circles and also to two sides of the square. Find the ratio between the area of the blue part and the area of the white part of the square.

B.

In the left-hand figure, there is a hexagon containing 6 circles with the same radius. Each circle is tangent to two other circles and also to one side of the hexagon, at its midpoint. Find the ratio between the area of the blue part and the area of the white part of the hexagon.

 

(Solution format: "x, y" for example "1/8, 7/100")

Difficulty level (1 very easy - 10 very hard): 1

Topics:
Geometry -> Area Calculation Geometry -> Plane Geometry -> Circles
Sources:
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