The problem of constructing, in a given plane, a circle tangent to three given circles. The circle representing the solution of this problem is known as Apollonius circle. The problem was named after Apollonius of Perge (3rd- century B.C.)

The routine returns a list of Apollonius circles. In general, there are eight circles.

Note that the coordinates of the centers and the radii of the circles must be numeric.

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

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

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

$\mathrm{circle}\left(\mathrm{c2}\,\left[\mathrm{point}\left(\mathrm{O1}\,6\,0\right)\,3\right]\,\left[x\,y\right]\right)\:$

$\mathrm{circle}\left(\mathrm{c3}\,x^2+{\left(y-7\right)}^2=1\,\left[x\,y\right]\right)\:$

$A≔\mathrm{Apollonius}\left(\mathrm{c1}\,\mathrm{c2}\,\mathrm{c3}\right)\:$

$\mathrm{draw}\left(A\right)$