Outer Pentagon Point
OuterPentagonPoint
Let A^' be the outermost vertex of the regular pentagon erected outward on side BC of a reference triangle DeltaABC. Similarly, define B^' and C^'. The triangle DeltaA^'B^'C^' is then perspective to DeltaABC, and the perspector is known as the outward pentagon point. It is Kimberling center X_(1139) and has equivalent triangle center functions
alpha_(1139) = [画像:(cscA)/(cotA-cot(2/5pi))]
(1)
![画像:1/(a[2Delta+tan(2/5pi)bccosA]),](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/OuterPentagonPoint/Inline14.svg){kind=link}
where Delta is the area of the reference triangle.
See also
Inner Pentagon PointExplore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Kimberling, C. "Encyclopedia of Triangle Centers: X(1139)=Outer Pentagon Point." https://faculty.evansville.edu/ck6/encyclopedia/ETCPart2.html#X1139.Referenced on Wolfram|Alpha
Outer Pentagon PointCite this as:
Weisstein, Eric W. "Outer Pentagon Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OuterPentagonPoint.html