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In geometry, the seven circles theorem is a theorem about a certain arrangement of seven circles in the
Interactive Applet
by Michael Borcherds showing The Seven Circles Theorem made usin
GeoGebra
the Seven Circles Theorem
by Stanley Rabinowitz, with a proof based on Ceva's theorems.
Seven Circles Theorem
at
In geometry, the seven circles theorem is a theorem about a certain arrangement of seven circles in the Euclidean plane
In mathematics, the Euclidean plane is a Euclidean space of dimension two. That is, a geometric setting in which two real quantities are required to determine the position of each point ( element of the plane), which includes affine notions of ...
. Specifically, given a chain of six circles all tangent to a seventh circle and each tangent to its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same point. Though elementary in nature, this theorem was not discovered until 1974 (by Evelyn, Money-Coutts, and Tyrrell).
See also
*Brianchon's theorem
In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. It is named after Charles Julien Brianchon (1 ...
* Theorem on friends and strangers
References
* * *External links
* {{MathWorld, title=Seven Circles Theorem, urlname=SevenCirclesTheoremInteractive Applet
by Michael Borcherds showing The Seven Circles Theorem made usin
GeoGebra
the Seven Circles Theorem
by Stanley Rabinowitz, with a proof based on Ceva's theorems.
Seven Circles Theorem
at
Cut-the-knot
Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician. He was Professor Emeritus of Mathematics at the University of Iowa, and formerly research fellow at the Moscow Institute of Electronics and Math ...
.
Theorems about circles