In Euclidean plane geometry, Lester's theorem states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle. The result is named after June Lester, who published it in 1997, [1] and the circle through these points was called the Lester circle by Clark Kimberling. [2]

In 1996, J. A. Lester discovered that in every scalene triangle the two Fermat-Torricelli points, the circumcenter, and the center of the nine- point circle are concyclic. We give the rst proof of this fact to only employ results from elementary geometry.

This remarkable theorem, due to Lester [1], asserts that in any scalene triangle the two Fermat points, the nine-point centre and the circumcentre are concyclic.

Aug 1, 2016 · This remarkable theorem, due to Lester, asserts that in any scalene triangle the two Fermat points, the nine-point centre and the circumcentre are concyclic. Lester’s original computer-assisted discovery and proof make use of her theory of ‘complex triangle coordinates’ and ‘complex triangle functions’ as expounded in, and .

In this paper is given an elementary proof of Lester’s theorem using the formulas for the distances between the points O, N, F+, F−. Also, using the properties of the orthocentroidal circle and cosymmedian triangles, other quadruples of concyclic points are indicated.

When P = X(3), it is well-know that Q(P ) = Q(X(3)) = X(5), the conjucture becomes Lester theorem. Theorem 3 (Parry).

This paper introduces another synthetic proof of Lester's theorem by showing that the two Fermat points are also the isodynamic points of the orthocentroidal triangle.

Lester’s theorem (1997) states that in any scalene triangle the two Fermat points F and F ' (to be defined later), the nine-point centre N , and the circumcentre O , are concyclic,...

Lester’s theorem (1997) states that in any scalene triangle the two Fermat points F and F ' (to be defined later), the nine-point centre N , and the circumcentre O , are concyclic, and that the...

In Euclidean plane geometry, Lester's theorem, named after June Lester, states that in any scalene triangle, the two Fermat points, the nine-point center, and the circumcenter lie on the same circle.