Convexity 1 - Homework 6

Undergraduate questions:

1. Lay Question 29.2
2. Prove that if A and B are sets of constant width then so is A+B
3. Let A and B be convex bodies in n-dimensional space. Prove that A is a subset of B if and only if the support function of A is at most that of B.
4. Let E be an ellipse in the plane. Prove that the circumscribed rectangles of E have their vertices on a fixed circle. (Circumscribed means each side of the rectangle is tangent to the ellipse).
5. 

Additional graduate questions:

6. Let K be set of constant width w and assume x is not in K. Prove that the diameter of the union of K and x is greater than w.
7. 
8.