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Circumtangential Triangle


CircumtangentialTriangle

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where X^(-1) is the isogonal conjugate, is tangent to the circumcircle (Kimberling 1998, p. 166).

Note that it is not in perspective with DeltaABC.

It has trilinear vertex matrix

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

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


See also

Circumnormal Triangle

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References

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

Referenced on Wolfram|Alpha

Circumtangential Triangle

Cite this as:

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

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