Chordal Theorem

$\begin{figure}\begin{center}\BoxedEPSF{RadicalAxis.epsf scaled 900}\end{center}\end{figure}$

The Locus of the point at which two given Circles possess the same Power is a straight line Perpendicular to the line joining the Midpoints of the Circle and is known as the chordal (or Radical Axis) of the two Circles.

References