The Lester circle is the circle on which the circumcenter , nine-point center , and the first and second Fermat points and lie (Kimberling 1998, pp. 229-230). Besides these (Kimberling centers , , , and , respective), no other notable triangle centers lie on the circle.

The Lester circle has circle function

(1)

where

(2)

does not appear to have a simple form and does not appear in Kimberling's list of triangle centers. The center of the Lester circle is

(3)

where is the circumradius of the reference triangle, which is Kimberling center . The radius of the Lester circle is given by

(4)

where is a symmetric 16th-order polynomial that does not appear to have a simple form.

It is orthogonal to the orthocentroidal circle.

Ahlschwede, T. "Lester's Circle Theorem." http://www.ops.org/north/curriculum/math/ahlsch/lester.htm.

Kimberling, C. "Lester Circle." Math. Teacher 89, 26, 1996.

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Lester, J. "Triangles III: Complex Triangle Functions." Aequationes Math. 53, 4-35, 1997.

Trott, M. "Applying GroebnerBasis to Three Problems in Geometry." Mathematica Educ. Res. 6, 15-28, 1997. http://library.wolfram.com/infocenter/Articles/1754/.

Trott, M. "A Proof of Lester's Circle Theorem." http://library.wolfram.com/infocenter/Demos/124/.

CITE THIS AS:

Weisstein, Eric W. "Lester Circle." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LesterCircle.html