Isosceles Triangle Containers of Triangles - 3

This post continues a somewhat old story narrated here and here . Note: the basic question was, given a general triangle T, to find the least area(perimeter) isosceles triangle that contains T.

Here is a preprint by Kiss, Pach and Somlai answering the question of finding the smallest isosceles (smallest area; smallest perimeter is pending) triangle container of any given triangle. Even as I try to work my way through it, let me record a couple of thoughts:

- In this post are pointers to works on these 2 questions: for a given convex polygon, find the least area (least perimeter) general triangle that contains it.

Questions:
- To find the least area isosceles triangle that contains a given convex polygon P: Will this work: 1)first find the least area general triangle that contains P and then 2) find the smallest area isosceles triangle that contains this least area general triangle container?

- Given any isosceles triangle T, how does one find that triangle of smallest area(perimeter) such that T is the least area(perimeter) isosceles triangle that contains it? Is the smallest convex region for which T is the smallest isosceles container necessarily a triangle? Note: here we are basically turning the original isosceles triangle container question inside out.

Note: All these thoughts can be floated with right triangles replacing isosceles. And what happens when one goes to Hyperbolic geometry?

Update (9th March 2020): One can also ask about covering a given general triangle T with 2 isosceles triangles with least total area. Then replace 2 by 3 and so on (Replacing isosceles by right makes this question trivial). Is this question related to finding the largest isosceles triangle that can be contained by T?