/sci/ - Science & Math

I have n convex sets in the euclidean plane, I take the first and second set, A and B respectively, and rotate and translate them over each other such that their intersection is maximized, now their UNION is a new set,let's call this new set (AB), we take the third set C and rotate and translate it such that it's intersection with set (AB) is maximized, this new set we call (ABC), we take the fourth set and do the same process with the previously generated set (ABC) to get set (ABCD), and we do this process
with all n sets, and end up with the set(ABC...n) which within itself contains all sets from A to n, the question is is the set (ABC... n) the same as the set that has minimum area but also contains all sets from a to n? PicRelated is an explicit example-