Jung's theorem states that every compact set $K \subset \Bbb{R}^n$ of diameter $d$ is contained in some closed ball of radius $$ r \leq d \sqrt{\frac{n}{2(n+1)}} $$ with equality attained for the regular $n$-simplex of side $d$.
Where can I find a proof of this result? The relevant page on Wikipedia mentions the original articles, which would be fine for me if they were in English, while none of the other references has a proof (at least not in full generality).
A discussion of (some of) its generalizations would be a nice bonus, too, but it isn't required.
A proof can be found for instance at https://matthewhr.wordpress.com/2013/03/14/hellys-theorem-and-applications-ii-jungs-theorem/, a sketch of the proof can be found in HTFB's answer to this MSE question.