On an Isoceles Triangle Question

About 2 years back, I posted a document at arxiv: https://arxiv.org/abs/1802.10447

The doc raised the following Basic question: Find the smallest area (smallest perimeter) isosceles triangle that contains a given general triangle.

Very recently, Gergely Kiss and Janos Pach wrote an abstract here: http://www.jcdcgg.u-tokai.ac.jp/JCDCG3_2019_abstracts_v1.pdf

Therein they have pointed out many subtle issues I had failed to appreciate. I look forward to the full manuscript (forthcoming) of their work and hope to learn more details of the problem.

For the time being, let me note this: I suspect there may be similar surprises if the largest area isosceles triangle CONTAINED WITHIN a given triangle is to be found. The largest PERIMETER isosceles triangle contained in a triangle could be degenerate for wide obtuse triangles.

I also hope the same questions with RIGHT TRIANGLES replacing isosceles ones (also mentioned without much insight in https://arxiv.org/abs/1802.10447) also are of interest.
And finally, what happens to all of the above in non Euclidean geometries? Admittedly, I can't do much there as yet.
Updates to follow: