There are $n$ random points in the $x-y$ plane, whose coordinates are known beforehand. We can use a minimum bounding rectangle (MBR) to bound these points. In this scenario, the MBR can be rotated, and I want to maximize the distance between a certain point $p$ (denoted by the red triangle) and the MBR.
It's clear that the distance varies with different rotation angles. For example, if we use the solid blue MBR to bound these points, then $p$ is inside this MBR, thus the distance is $0$. On the other hand, if we take the dashed green rectangle as MBR, the distance increases.
I want to know how to compute the optimal rotation angle that maximizes the distance between $p$ and the corresponding MBR, or is this possible in the first place? Since, intuitively, as the MBR rotates, those points on the boundary will also change in a rather random manner, it's hard to predict how the distance will vary.