Far-Out Point

For a Triangle with side lengths $a$, $b$, and $c$, the far-out point has Triangle Center Function

$$\alpha=a(b^4+c^4-a^4-b^2 c^2).$$

As $a:b:c$ approaches $1:1:1$, this point moves out along the Euler Line to infinity.

References

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

Kimberling, C.; Lyness, R. C.; and Veldkamp, G. R. ``Problem 1195 and Solution.'' Crux Math. 14, 177-179, 1988.