Convex Figures I.M. Yaglom and V.G. Boltyanskii Holt, Rinehart and Winston, NY, 1961
The first half of this book has definitions and results related to convexity to be proved by the reader and the solutions to these problems (theorems) is given in the second half of the book.
The topics treated include Helly's Theorem, isoperimetric results, Minkowski addition of sets and curves of constant width.
All of this material is clearly and well handled.