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Yff Contact Circle

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YffContactCircle

The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function

alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a,
(1)

which does not correspond to any Kimberling center.

Its radius is

R_Y=1/(2|(a-b)(b-c)(c-a)|)sqrt((f(a,b,c)f(b,c,a)f(c,a,b))/(a+b+c)),
(2)

where

f(a,b,c)=a^3-2ca^2+bca+b^3+c^3-2b^2c.
(3)

Its circle function is

l=-(a^4-a^3b+ab^3-b^4-a^3c+a^2bc-ab^2c+b^3c-abc^2+ac^3+bc^3-c^4)/(2bc(a-b)(a-c)),
(4)

which does not correspond to any Kimberling center.

Kimberling center X_(1281) lies on this circle.

The orthocenter of the Yff contact triangle is the Nagel point of the reference triangle.

See also

Central Circle, Yff Contact Triangle

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Cite this as:

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

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