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Outer Vecten Circle


OuterVectenCircle

The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point X_(485) and has triangle center function

 alpha_(641)=(a^2bc(3cosA+2cosBcosC)+2(b^2+c^2)Delta)/a,

where Delta is the area of the reference triangle, and its radius is a slightly complicated expression. Its circle function is

 l=-4a^3Delta[Delta+2bccos(B-C)].

No Kimberling centers lie on the circle.


See also

Inner Vecten Circle, Outer Vecten Triangle

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Cite this as:

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

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