This question already has an answer here:
The question Finding third side of a minimal triangle appears to be essentially a duplicate of https://stackoverflow.com/questions/22441855/triangle-circle-enclosing-a-set-of-points .
The stackoverflow question has detailed answers with references, for this nontrivial problem.
If it is a duplicate (which is not yet entirely clear, since the question is itself not entirely clear), should it be closed (I think yes), and if so, how? The option to close as duplicate does not work -- it says "The duplicate question must exist on Mathematics Stack Exchange".
(Sorry if this has been asked before, but I couldn't find it -- just close as a duplicate if it has!)