The routine finds the tangent line(s) of point P with respect to circle c

The output is obj which is assigned to a list of two lines (two tangent lines), or a line (one tangent line), or nothing (there is no tangent).

If the third optional argument is given and in case there exists two tangent lines, the names of the tangent lines are the two elements in the list.

For more details on the tangent, use detail.

The command with(geometry,TangentLine) allows the use of the abbreviated form of this command.

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

$\mathrm{point}\left(A\,1\,1\right),\mathrm{circle}\left(c\,a^2+b^2=1\,\left[a\,b\right]\right)$

$A,c$

$\mathrm{TangentLine}\left(\mathrm{obj}\,A\,c\,\left[\mathrm{l1}\,\mathrm{l2}\right]\right)$

$\left[\mathrm{l1}\,\mathrm{l2}\right]$

$\mathrm{form}\left(\mathrm{l1}\right),\mathrm{Equation}\left(\mathrm{l1}\right)$

$\mathrm{line2d},-1+a=0$

$\mathrm{form}\left(\mathrm{l2}\right),\mathrm{Equation}\left(\mathrm{l2}\right)$

$\mathrm{line2d},1-b=0$