  In this paper we study circles tangent to conics. We show there are
generically $184$ complex circles tangent to three conics in the plane and we
characterize the real discriminant of the corresponding polynomial system. We
give an explicit example of $3$ conics with $136$ real circles tangent to them.
We conjecture that 136 is the maximal number of real circles. Furthermore, we
implement a hill-climbing algorithm to find instances of conics with many real
circles, and we introduce a machine learning model that, given three real
conics, predicts the number of circles tangent to these three conics.
