Assume I have an $n$-dimensional simplex on the points $x_0, ..., x_n$ where each $x_i \in \mathbb{R}^n$. I would like to obtain the parameters (center and radius) of it's circumscribed n-dimensional hypershpere. How do I do that?

I found the formulas for circle and ordinary shpere, but I am not sure how to generalize that properly.