The power of point P with respect to sphere s is $-R^2+d^2$ where d is the distance from point P to the center of s, and R is the radius of s.

The command with(geom3d,powerps) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{point}\left(o\&comma;X\&comma;Y\&comma;Z\right)\&colon;$$\mathrm{assume}\left(0<k\right)\&colon;$

$\mathrm{sphere}\left(s\&comma;\left[o\&comma;k\right]\right)\&colon;$

$\mathrm{point}\left(P\&comma;\left[\mathrm{x1}\&comma;\mathrm{y1}\&comma;\mathrm{z1}\right]\right)\&colon;$

$\mathrm{powerps}\left(P\&comma;s\right)$

${\left(X-\mathrm{x1}\right)}^2+{\left(Y-\mathrm{y1}\right)}^2+{\left(Z-\mathrm{z1}\right)}^2-{\mathrm{k~}}^2$