The locus of a point whose powers with respect to two given circles are equal is called the radical axis of the two given circles.

Note that the routine in particular, and the geometry package in general, does not work with extended plane, i.e. the radical axis of two concentric circles does not exist (though in extended plane, when c1 and c2 are concentric but not equal, the radical axis is frequently defined to be the line at infinity in the plane of the circles, and the radical axis of two equal concentric circles is left undefined.)

For a detailed description of the radical axis l, use the routine detail (e.g., detail(l))

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

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

$\mathrm{circle}\left(\mathrm{c1}\,x^2+y^2=1\,\left[x\,y\right]\right),\mathrm{circle}\left(\mathrm{c2}\,\left[\mathrm{point}\left(A\,3\,3\right)\,4\right]\,\left[x\,y\right]\right)\:$

$\mathrm{RadicalAxis}\left(l\,\mathrm{c1}\,\mathrm{c2}\right)$

$l$

$\mathrm{form}\left(l\right)$

$\mathrm{line2d}$

$\mathrm{Equation}\left(l\right)$

$-3+6x+6y=0$