Largest Circular Segment Within Closed Curve

[Joshua_Halliday]

This might be a long shot, but I’m looking for the best way to find the largest possible circular segment within a closed curve, like the diagram below:

I have a couple of constraints, mainly being that the arc needs to face roughly towards the Y direction (upwards). If anyone has any ideas on how to do this using Grasshopper, it would be appreciated.

[davidcockey]

Largest as in:
Longest arc length?
Largest radius?
Largest curvature (smallest radius)?
Something else?

“within a closed curve”
Do you want an arc which is part of the closed curve, or which lies within the curve?

[anon39580149]

Do you need the arc between the corners or any points?