Five circles theorem

Short description: Derives a pentagram from five chained circles centered on a common sixth circle

In geometry, the five circles theorem states that, given five circles centered on a common sixth circle and intersecting each other chainwise on the same circle, the lines joining their second intersection points forms a pentagram whose points lie on the circles themselves.

See also

• Clifford's circle theorems
• Miquel's theorem
• Six circles theorem
• Seven circles theorem

References

• Wells D (1991). The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin Books. pp. 79. ISBN 0-14-011813-6. https://archive.org/details/penguindictionar0000well/page/79. 

External links

• Weisstein, Eric W.. "Miquel Five Circles Theorem". http://mathworld.wolfram.com/MiquelFiveCirclesTheorem.html. 
• Weisstein, Eric W.. "Miquel Pentagram Theorem". http://mathworld.wolfram.com/MiquelsPentagramTheorem.html.