In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the Bankoff circle or Bankoff triplet circle is a certain
Archimedean circle that can be constructed from an
arbelos
In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...
; an Archimedean circle is any circle with area equal to each of
Archimedes' twin circles. The Bankoff circle was first constructed by
Leon Bankoff in 1974.
[.]
Construction
The Bankoff circle is formed from three
semicircle
In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180° (equivalently, radians, or a half-turn). It only has one line of symmetr ...
s that create an
arbelos
In geometry, an arbelos is a plane region bounded by three semicircles with three apexes such that each corner of each semicircle is shared with one of the others (connected), all on the same side of a straight line (the ''baseline'') that conta ...
. A circle ''C''
1 is then formed tangent to each of the three semicircles, as an instance of the
problem of Apollonius. Another circle ''C''
2 is then created, through three points: the two points of tangency of ''C''
1 with the smaller two semicircles, and the point where the two smaller semicircles are tangent to each other. ''C''
2 is the Bankoff circle.
Radius of the circle
If ''r'' = ''AB''/''AC'', then the radius of the Bankoff circle is:
:
References
External links
* {{MathWorld, title=Bankoff Circle, urlname=BankoffCircle
Bankoff Circleby Jay Warendorff, the
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an Open source, open-source collection of Interactive computing, interactive programmes called Demonstrations. It is hosted by Wolfram Research. At its launch, it contained 1300 demonstrations but has grown t ...
.
Online catalogue of Archimedean circles Floor van Lamoen.
Arbelos
Elementary geometry