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Far-Out Point


Far-OutPoint

The far-out point F of a triangle DeltaABC is the inverse point of the triangle centroid with respect to the circumcircle of DeltaABC. 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^2c^2).

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


See also

Circumcircle, Inverse Points, Triangle Centroid

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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.

Referenced on Wolfram|Alpha

Far-Out Point

Cite this as:

Weisstein, Eric W. "Far-Out Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Far-OutPoint.html

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