For a 2-dimensional closed convex shape $C$, define:
- $d(C)$ = the diameter of $C$ (the largest distance between two points in $C$).
- $D(C)$ = the diameter of the smallest circle containing $C$.
Often $d(C)=D(C)$, for example in a unit square they are both $\sqrt 2$.
Sometimes $d(C)<D(C)$, for example in a unit equilateral triangle $d(C)=1$ and $D(C)=2/\sqrt 3$.
MY QUESTION: What is the largest value of $D(C)/d(C)$? (Can it be larger than $2/\sqrt 3$?)