In a square with a side length of 1, two quarter circles are drawn and a circle is inscribed between the quarter circles, as shown in the diagram.
What is the radius of the inscribed circle?

A square contains a semicircle and a quarter circle, as shown. The two circles are tangent to each other. The semicircle has a diameter equal to 12 and the quarter circle has a radius equal to 12.
What is the area of the square?
What is the length of the tangent line segment AB?

Two circles are drawn inside a square with side length 2 + SQRT(2) as shown in the figure. Let the radius of the larger circle be R and the radius of the smaller circle be r . Find the value of R + r