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Second Fermat Point

InnerNapoleonsTheorem

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and connecting opposite vertices. The three diagonals in the figure then intersect in the second Fermat point, which has triangle center function

alpha=csc(A-1/3pi)

and is Kimberling center X_(14) (Kimberling 1998, p. 68).

It also arises in Napoleon's theorem.

See also

Fermat Axis, Fermat Points, First Fermat Point, Napoleon's Theorem

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Encyclopedia of Triangle Centers: X(14)=2nd Isogonic Center." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X14.

Referenced on Wolfram|Alpha

Second Fermat Point

Cite this as:

Weisstein, Eric W. "Second Fermat Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SecondFermatPoint.html

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