Given a triangle , the Thomson cubic of is the set of the centers of circumconics whose normals at the vertices are concurrent [2]. It is a self-isogonal cubic with pivot point at the triangle centroid.

Let , , be the side lengths of the reference triangle and , , be the excenters. Then the equation of the Thomson cubic of triangle in barycentric coordinates is

, where indicates that the sum is taken over all six permutations of , , .

The solution is traced in red. Some of the Kimberling centers on the Thomson cubic are:

, , , , , , , , , , , , , , , , , [3].

You can drag the vertices , and .