I have three touching circles, and I was trying to find the point inbetween them that is equally far from all three circles. So I created a system of equations:
$$ \begin{array}{lcl} (x-x1)^2 + (y-y1)^2=(r+r1)^2 \\ (x-x2)^2 + (y-y2)^2=(r+r2)^2 \\ (x-x3)^2 + (y-y3)^2=(r+r3)^2 \end{array} $$
$x1, x2, x3, y1, y2, y3, r1, r2, r3$ are the coordinates of the 3 circles and their radii. $x, y$ are the x-and y-coordinate of the point I'm looking for. $r$ is the distance of that point to each circle.
It seems like a simple system, but apparently it's not. Could anyone help me with solving the problem?
Also, a more general solution could be useful, where the initial three circles don't have to touch (but don't overlap). Then I would need to find the biggest circle that can fit in between them, without overlapping any.
Thanks!