The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known as the chordal (or, more commonly, the radical line) of the two circles.
Chordal Theorem
See also
Circle Power, Radical LineExplore with Wolfram|Alpha
References
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 153, 1965.Referenced on Wolfram|Alpha
Chordal TheoremCite this as:
Weisstein, Eric W. "Chordal Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChordalTheorem.html