Apollonius - Maple Help

geometry

 Apollonius
 find the Apollonius circles of three given circles

 Calling Sequence Apollonius(c1, c2, c3)

Parameters

 c1, c2, c3 - three circles

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{circle}\left(\mathrm{c1},{\left(x+3\right)}^{2}+{y}^{2}=4,\left[x,y\right]\right):$
 > $\mathrm{circle}\left(\mathrm{c2},\left[\mathrm{point}\left(\mathrm{O1},6,0\right),3\right],\left[x,y\right]\right):$
 > $\mathrm{circle}\left(\mathrm{c3},{x}^{2}+{\left(y-7\right)}^{2}=1,\left[x,y\right]\right):$
 > $A≔\mathrm{Apollonius}\left(\mathrm{c1},\mathrm{c2},\mathrm{c3}\right):$
 > $\mathrm{draw}\left(A\right)$