Five Circles Theorem

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Five circles have centers on a fixed circle with radii such that each intersects its two neighbors on the fixed circle. Then their other points of intersection give rise to the sides of a star polygon with vertices on the five circles. The radii of the first four circles can be picked at random as long as the circles complete the chain.

Contributed by: Borut Levart (May 2014)
Open content licensed under CC BY-NC-SA



Click the button to pick circle radii at random.


[1] D. Wells, The Penguin Dictionary of Curious and Interesting Geometry, London: Penguin, 1991.

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