Problem 1072

Maya the Bee is very proud to appear on the logo of this beekeeping company.



In this square of 20 cm × 20 cm where his portrait is inscribed, his wings in the form of moons are limited by:

• two half-circles having for diameters two of its sides
• and a quarter circle having for radius the side of the square, centered at a vertex of the square.

The three arcs of a circle intersect each other in three points, through which passes precisely the little yellow circle of its abdomen. As for its head, it is represented by the large yellow circle tangent at the same time to two sides of the square and to the two preceding half-circles.

• 1. What is the radius of the great yellow circle representing its head? (9 points)
  
  
• 2. What is the radius of the small yellow circle representing its abdomen? (9 points)

(We will give the answers in cm, rounded to two decimals, separating the decimals by a point or a comma.)

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