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Inner Pentagon Point

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InnerPentagonPoint

Let A^' be the outermost vertex of the regular pentagon erected inwards 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 inner pentagon point. It is Kimberling center X_(1140) and has equivalent triangle center functions

alpha_(1140)=(cscA)/(cotA+cot(2/5pi))
(1)
alpha_(1140)=1/(a[2Delta-tan(2/5pi)bccosA]),
(2)

where Delta is the area of the reference triangle.

See also

Outer Pentagon Point

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References

Kimberling, C. "Encyclopedia of Triangle Centers: X(1140)=Inner Pentagon Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X1140.

Referenced on Wolfram|Alpha

Inner Pentagon Point

Cite this as:

Weisstein, Eric W. "Inner Pentagon Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InnerPentagonPoint.html

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