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d'Alembert's Theorem

If three Circles $A$, $B$, and $C$ are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one pair and the two internal similarity points of the other two pairs lie upon a straight line, forming a similarity axis of the three Circles.


Dörrie, H. 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, p. 155, 1965.

© 1996-9 Eric W. Weisstein