Problem of Apollonius
It is generically possible to construct such a circle in $8$ different ways.
Source of Name
This entry was named for Apollonius of Perga.
While this in itself is a remarkable feat, the fact that she achieved it using Descartes' own methods makes it more impressive, as these are not the easiest tools to use to attack the problem.
However, Descartes appears to have been unfairly and cruelly dismissive of her achievement