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Circumnormal Triangle


CircumnormalTriangle

The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by pi/6 radius about its circumcenter (Kimberling 1998, pp. 166-167). Note that it is not in perspective with DeltaABC.

It has trilinear vertex matrix

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

All triangle centers of the circumnormal triangle correspond to the circumcenter of the reference triangle.


See also

Circumtangential Triangle

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References

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

Referenced on Wolfram|Alpha

Circumnormal Triangle

Cite this as:

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

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