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Hexyl Circle


HexylCircle

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function is

 l=-(a^4-2ba^3-2ca^3+2b^3a+2c^3a-2bc^2a-2b^2ca-b^4-c^4+2b^2c^2)/(4Delta^2),

where Delta is the area of the reference triangle, which is not a Kimberling center.

No Kimberling centers lie on it.


See also

Central Circle, Hexyl Triangle

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Cite this as:

Weisstein, Eric W. "Hexyl Circle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HexylCircle.html

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