If the Vertices , , and of Triangle lie on sides , , and of the Triangle , then the three Circles , , and have a common point. In extended form, it is Miquel's Theorem.
See also Miquel's Theorem
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.