  We call an order type inscribable if it is realized by a point configuration
where the extreme points are all on a circle. In this paper, we investigate
inscribability of order types. We first show that every simple order type with
at most 2 interior points is inscribable, and that the number of such order
types is $\Theta(\frac{4^n}{n^{3/2}})$. We further construct an infinite family
of minimally uninscribable order types. The proof of uninscribability mainly
uses M\"obius transformations. We also suggest open problems around
inscribability.
