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GeezerVison is showing mathworld.wolfram.com — Second Yff Circles Triangle -- from Wolfram MathWorld

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Second Yff Circles Triangle


The second Yff circles triangle is the triangle formed by the centers of the second triplet of Yff circles. It is homothetic to the reference triangle at its incenter, with directed scale factor h=r/(r-R), where r and R are the inradius and circumradius of the reference triangle, respectively (F. M. Jackson, pers. comm., June 7, 2007).

The following table gives the centers of the second Yff circles triangle in terms of the centers of the reference triangle for Kimberling centers X_n with n<=100.

X_ncenter of second Yff circles triangleX_ncenter of reference triangle
X_1incenterX_1incenter
X_3circumcenterX_(56)external similitude center of circumcircle and incircle
X_4orthocenterX_(1479)(X_1,X_4)-harmonic conjugate of X_(1478)
X_5nine-point centerX_(496)(X_1,X_5)-harmonic conjugate of X_(495)
X_6symmedian pointX_(613)intersection of lines X_1X_6 and X_(56)X_(511)
X_(10)Spieker centerX_(1210)isogonal conjugate of X_(1167)
X_(40)Bevan pointX_(46)X_4-Ceva conjugate of X_1

See also

First Yff Circles Triangle, Yff Circles

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Cite this as:

Weisstein, Eric W. "Second Yff Circles Triangle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SecondYffCirclesTriangle.html

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