If the vertices 
,
, and 
of triangle 
lie on sides 
, 
,
and 
of the triangle 
, then the three circumcircles 
, 
, and 
have a common point 
. In extended form, this theorem becomes Miquel's
theorem.
Pivot Theorem
See also
Circumcircle, Clifford's Circle Theorem, Miquel's TheoremExplore with Wolfram|Alpha
References
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. New York: Random House, pp. 61-62, 1967.Forder, H. G. Geometry. London: Hutchinson, p. 17, 1960.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 184, 1991.Referenced on Wolfram|Alpha
Pivot TheoremCite this as:
Weisstein, Eric W. "Pivot Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PivotTheorem.html