Approximation of Spherical Bodies of Constant Width and Reduced Bodies

We present a spherical version of the theorem of Blaschke that every body of constant width w < π/2 can be approximated by a body of constant width w whose boundary consists only of pieces of circles of radius w as well as we wish in the sense of the Hausdorff distance. This is a special case of our theorem about approximation of spherical reduced bodies.