Max intersecting circle collection

Question

Given any collection of $n$ distinct circles in the plane (with fixed but possibly distinct radii),

is it always possible to rearrange the circles so that any two of them intersect twice?

Answer 1

Yes.

Arrange the circles such that they all share one point $P$, and that any pair of centers are not collinear with $P$.

Any pair of circles will now intersect at $P$ and one other point that is the reflection of $P$ across the line between the circles' centers.