The pivot theorem states that 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.

See also

Circumcircle, Clifford's Circle Theorem, Miquel's Theorem

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References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. New York: Random House, pp. 61-62, 1967.Forder, H. G. Geometry. London, England: Hutchinson, p. 17, 1960.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London, England: Penguin, p. 184, 1991.

Referenced on Wolfram|Alpha

Pivot Theorem

Cite this as:

Weisstein, Eric W. "Pivot Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PivotTheorem.html

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