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Miquel Circles

\begin{figure}\begin{center}\BoxedEPSF{MiquelsTheorem.epsf scaled 950}\end{center}\end{figure}

For a Triangle $\Delta ABC$ and three points $A'$, $B'$, and $C'$, one on each of its sides, the three Miquel circles are the circles passing through each Vertex and its neighboring side points (i.e., $AC'B'$, $BA'C'$, and $CB'A'$). According to Miquel's Theorem, the Miquel circles are Concurrent in a point $M$ known as the Miquel Point. Similarly, there are $n$ Miquel circles for $n$ lines taken $(n-1)$ at a time.

See also Miquel Point, Miquel's Theorem, Miquel Triangle

© 1996-9 Eric W. Weisstein