The routine returns true if the plane p is tangent to the sphere s; false if they are not; and FAIL if it is unable to reach a conclusion.

In case of FAIL, if the third optional argument is given, the condition that makes p tangent to s is assigned to this argument.

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

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

$\mathrm{sphere}\left(s\,\left[\mathrm{point}\left(o\,0\,0\,1\right)\,1\right]\right)$

$s$

$\mathrm{assume}\left(a\ne 0\right)$

$\mathrm{plane}\left(p\,ax+by+cz+d=0\,\left[x\,y\,z\right]\right)$

$p$

$\mathrm{IsTangent}\left(p\,s\,'\mathrm{condition}'\right)$

IsTangent:   "unable to determine if 1-abs(c+d)/(a^2+b^2+c^2)^(1/2) is zero"

$\mathrm{FAIL}$

$\mathrm{condition}$

$1-\frac{\left|c+d\right|}{\sqrt{{\mathrm{a~}}^2+b^2+c^2}}=0$