Schiffler Point

The Concurrence $S$ of the Euler Lines $E_n$ of the Triangles $\Delta XBC$, $\Delta XCA$, $\Delta XAB$, and $\Delta ABC$ where $X$ is the Incenter. The Triangle Center Function is

$$\alpha={1\over \cos B+\cos C}={b+c-a\over b+c}.$$

References

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

Kimberling, C. ``Schiffler Point.'' http://cedar.evansville.edu/~ck6/tcenters/recent/schiff.html.

Schiffler, K.; Veldkamp, G. R.; and van der Spek, W. A. ``Problem 1018 and Solution.'' Crux Math. 12, 176-179, 1986.