de Longchamps Point

The reflection of the Orthocenter about the Circumcenter. This point is also the Orthocenter of the Anticomplementary Triangle. It has Triangle Center Function

$$\alpha=\cos A-\cos B\cos C.$$

It lies on the Euler Line.

References

Altshiller-Court, N. ``On the de Longchamps Circle of the Triangle.'' Amer. Math. Monthly 33, 368-375, 1926.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Vandeghen, A. ``Soddy's Circles and the de Longchamps Point of a Triangle.'' Amer. Math. Monthly 71, 176-179, 1964.