Jung's Theorem in the Plane

Theorem
Let $S \subseteq \R^2$ be a compact region in a Euclidean plane.

Let $d$ be the diameter of $S$.

Then there exists a circle $C$ with radius $r$ such that:
 * $r = d \dfrac {\sqrt 3} 3$

such that $S \subseteq C$.

The parameter $\dfrac {\sqrt 3} 3$ can also be presented as $\dfrac 1 {\sqrt 3}$, and evaluates approximately as:
 * $\dfrac {\sqrt 3} 3 \approx 0 \cdotp 57735 \, 02691 \ldots$

Proof
This is an instance of Jung's Theorem, setting $n = 2$.