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First Morley Adjunct Triangle


MorleysTriangle

The first Morley adjunct triangle is the triangle DeltaA^('')B^('')C^('') illustrated above, where DeltaA^'B^'C^' is the first Morley triangle. Unlike the first Morley triangle, the first Morley adjunct triangle is not equilateral.

The first Morley adjunct triangle has trilinear vertex matrix

 [2 sec(1/3C) sec(1/3B); sec(1/3C) 2 sec(1/3A); sec(1/3B) sec(1/3A) 2]

(Kimberling 1998, p. 167).

The first Fermat point of the first Morley adjunct triangle is the first Morley center X_(356).


See also

First Morley Triangle, Second Morley Adjunct Triangle, Third Morley Adjunct Triangle

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

Referenced on Wolfram|Alpha

First Morley Adjunct Triangle

Cite this as:

Weisstein, Eric W. "First Morley Adjunct Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FirstMorleyAdjunctTriangle.html

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