Salinon

This shape, which is constructed using four semi-circles, is called a Salinon.

If the radius of the larger blue semicircle is a and the radius of the smaller blue semicircle is b, what are the radii of the smallest semicircles?

What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

See the Notes for Teachers.

See the similar problems Round and Round and Partly Circles on NRICH.