Bankoff circle

Bankoff circle

In geometry, the Bankoff circle, which is equal in area to each of Archimedes' twin circles (making it an Archimedean circle, was created by Leon Bankoff. [Mathematics Magazine vol. 47 (1974) pp. 214–218]

Construction

The Bankoff circle created by with three semicircles that create an arbelos. A circle is then formed with three of its points "Pi" tangent to each semicircle. Another circle is then created with three of its points being the cusp formed by the two inner semicircles and the two intersecting points between the first circle and the two inner semicircles.

Radius of the circle

If "r" = "AB"/"AC", then the radius of the Bankoff circle is:

:R=frac{1}{2}rleft(1-r ight).

Notes

References

*

External links

* [http://demonstrations.wolfram.com/BankoffCircle/ Bankoff Circle] by Jay Warendorff, The Wolfram Demonstrations Project.


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