Adam Majewski wrote:
>eq12: (x1-x2)^2 + (y1 -y2)^2 - (r1-r2)^2;
I think you mean (r1+r2)^2 here and in the other two equations. In fact, you don't really need eq12. You can solve it like this:
eq13:(x1-x3)^2+(y1-y3)^2-(r1+r3)^2;
eq23:(x2-x3)^2+(y2-y3)^2-(r2+r3)^2;
solve([eq13,eq23],[x3,y3]);
Maxima returns:
[[x3=0,y3=50-50*sqrt(3)],[x3=0,y3=50*sqrt(3)+50]]
These represent, of course, the two possible tangent circles (above and below).
Ed