Thank you for this comment, it's really great! The algorithm you proposed would definitely work perfectly for a circle, but I think that there might be a corner case in which the first furthest point (B in your nomenclature) would not be one of the two furthest points in general, because of the shape of the points.

Please take a look at this image: https://imgur.com/a/FFZdAYW

There is a point at the upper left arm of this shape, for which the furthest point is the far-right tip of the arm, while the two furthest points are actually the top left tip and the bottom one. That said, if precision is not an issue, this could be a very good fast approximation!