Suppose I have 2 circles that intersect tangentially, and I'm looking at the set of all points within both circles. For example, the set of all
$(x,y)$ such that $$(x-2)^2+y^2 \le 4$$ or $$(x+3)^2+y^2 \le 9$$
Looking at the boundary of this region, is there a special topological term for the type of boundary point the origin is here (where the boundary crosses itself)?
Two tangent circles are not homeomorphic to a circle because the former has a cutpoint, the point of tangency, and the latter has none.