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 TriangleExplore with Wolfram|Alpha
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References
Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Referenced on Wolfram|Alpha
Circumnormal TriangleCite this as:
Weisstein, Eric W. "Circumnormal Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CircumnormalTriangle.html