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## Outline of Proof  We're going to prove by contradiction. We assume that \(p,q\) have maximum pairwise distance, and that one of \(p\) or \(q\) lies in the interior of the convex hull. We can extend the line and hit a point on the boundary of the convex plane. Clearly this point on the boundary is further from our original point. Furthermore, we can 'slide' along the edge we've discovered in a direction which ensures that our distance along this line is monotonically increasing. The proof is complete with the observation that this 'slide' has to end up at a vertex.  - MISC SPIE is fine - CV is OK too