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# Third Morley Triangle

The third Morley triangle is made by rotating line toward vertex about vertex by angle . It is an equilateral triangle.

It has trilinear vertex matrix

 (1)

(Kimberling 1998, p. 165).

Its signed side lengths are

 (2)

giving an area of

 (3)

The following table lists perspectors of the third Morley triangles with other named triangles that are Kimberling centers.

 triangle Kimberling perspector first Morley triangle 4th Morley-Taylor-Marr center reference triangle third Morley-Taylor-Marr center second Morley triangle 6th Morley-Taylor-Marr center

First Morley Triangle, Second Morley Triangle

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## References

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

## Referenced on Wolfram|Alpha

Third Morley Triangle

## Cite this as:

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