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# Yff Center of Congruence

Begin with the Yff central triangle and then parallel-displace the isoscelizers in such a way as to reduce the central triangle to a point while keeping the other three triangles congruent to each other. The point thus constructed is called the Yff center of congruence, and has triangle center function

 (1)

By analogy with the determination of the Yff central triangle, the angle is related to the isoscelizer distance and the inner triangle side lengths are given by

 (2)

and so on. Therefore, the length and can be determined by solving the six simultaneous equations

 (3) (4) (5) (6) (7) (8)

Congruent Isoscelizers Point, Isoscelizer, Yff Central Triangle

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## References

Kimberling, C. "Yff Center of Congruence." http://faculty.evansville.edu/ck6/tcenters/recent/yffcc.html.

## Referenced on Wolfram|Alpha

Yff Center of Congruence

## Cite this as:

Weisstein, Eric W. "Yff Center of Congruence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/YffCenterofCongruence.html