Wikipedia references: Curve of constant width, Reuleaux polygon.

We record a pair of questions on the same lines as Smallest 3-ellipses that contain triangles.

**Questions:**

How does one find and characterize the

*smallest curves of constant width*that contain a given triangle? 'Smallest' can mean 'least area' or 'least perimeter' or... and may have different answers. We consider only convex constant width curves.And what about the largest constant width curves that are contained in a given triangle?

*Guess:* The largest area constant width curve contained in any triangle might be a (possibly irregular) Reuleux polygon. The contained constant width curve with largest perimeter may not be formed of circular arcs.

**Note added on October 18th, 2023:** We can also ask inside-out versions of these questions; for example, given a constant width curve, is the triangle for which it is the smallest containing/ largest embedded constant width curve unique? How to find it/them?