The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the same circle power and at which all the tangency secants intersect.
Tangency Theorem
Explore with Wolfram|Alpha
References
Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 157, 1965.Referenced on Wolfram|Alpha
Tangency TheoremCite this as:
Weisstein, Eric W. "Tangency Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TangencyTheorem.html