Given two overlapping hyperspheres with known centers and radii, is there a way to enclose them inside a wider hypersphere in a way that it "touches" the two inside hyperspheres only at their outmost points, like in the picture below?
Is there a formula that gives the outside hypersphere?
Thank you
Sure. If the centers and radii are $(\mathbf{x}_A, r_A)$ and $(\mathbf{x}_B, r_B)$, and the distance between the centers is $|\mathbf{x}_A - \mathbf{x}_B|=d_{AB}$, then the radius of the enclosing hypersphere is going to be $R=(d_{AB}+r_A+r_B)/2$, and its center will be $$\mathbf{x}_A + \frac{R-r_A}{d_{AB}}\left(\mathbf{x}_B - \mathbf{x}_A\right).$$