Bankoff circle

In geometry, the Bankoff circle or Bankoff triplet circle is a certain Archimedean circle that can be constructed from an arbelos; an Archimedean circle is any circle with area equal to each of Archimedes' twin circles.

[1][2][3] The Bankoff circle is formed from three semicircles that create an arbelos.

A circle C1 is then formed tangent to each of the three semicircles, as an instance of the problem of Apollonius.

Another circle C2 is then created, through three points: the two points of tangency of C1 with the smaller two semicircles, and the point where the two smaller semicircles are tangent to each other.

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

A Bankoff circle with the center C' ' 6