Lester's theorem

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] Lester proved the result by using the properties of complex numbers; subsequent authors have given elementary proofs[3][4][5][6], proofs using vector arithmetic,[7] and computerized proofs.[8]

The Fermat points ${\displaystyle X_{13},X_{14}}$, the center ${\displaystyle X_{5}}$ of the nine-point circle (light blue), and the circumcenter ${\displaystyle X_{3}}$ of the green triangle lie on the Lester circle (black).