Enclosing and Embedded isosceles triangles for a triangle - orientations

In this paper: https://arxiv.org/pdf/2205.11637.pdf, the following questions are answered:

- Given a triangle, how to find the smallest area(perimeter) isosceles triangle that contains it?

- Given a triangle, how to find the largest area(perimeter) isosceles triangle contained in it?

Let me just record a pair of associated questions for which the answer might be readily obtained from the above paper:

Which is the triangle for which the smallest area (perimeter) isosceles container and largest area (perimeter) isosceles containee have angular difference between their orientations is maximum? The orientation of an isosceles triangle is given treating the triangle as an arrowhead - from the midpoint of its base towards the apex.

A further pair of questions:
Which is the convex polygon for which the smallest area (perimeter) rectangle that contains it and the largest area (perimeter) rectangle contained in it have the angular difference between their orientations a maximum? The orientation of a rectangle is naturally its length or width - for a square, one could take either as orientation.

The answers for the above should be available soon. I shall update this post when they reach me.