Suppose we are working in $\mathbb{R}^3$ space and we have four non-coplanar and non-collinear points, $(x_a, y_a, z_a)$, $(x_b, y_b, z_b)$, $(x_c,y_c, z_c)$, and $(x_d, y_d, z_d)$. How does one determine the coordinates of the center of the circumsphere and the center of the insphere of these points?

Suppose we are working in $\mathbb{R}^3$ space and we have four non-coplanar and non-collinear points, $(x_a, y_a, z_a)$, $(x_b, y_b, z_b)$, $(x_c,y_c, z_c)$, and $(x_d, y_d, z_d)$. How does one determine the coordinates of the center of the circumsphere and the center of the insphere of these points, and what are the formulae for these points?

Suppose we are working in $\mathbb{R}^3$ space and we have four non-coplanar and non-collinear points, $(x_a, y_a, z_a), (x_b, y_b, z_b), (x_c,y_c, z_c),$ and $(x_d, y_d, z_d)$. How does one determine the coordinates of the center of the circumsphere and the center of the insphere of these points?

Suppose we are working in $\mathbb{R}^3$ space and we have four non-coplanar and non-collinear points, $(x_a, y_a, z_a)$, $(x_b, y_b, z_b)$, $(x_c,y_c, z_c)$, and $(x_d, y_d, z_d)$. How does one determine the coordinates of the center of the circumsphere and the center of the insphere of these points?