Pivot Theorem

If the Vertices $A$, $B$, and $C$ of Triangle $\Delta ABC$ lie on sides $QR$, $RP$, and $PQ$ of the Triangle $\Delta PQR$, then the three Circles $CBP$, $ACQ$, and $BAR$ 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.