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# Yff Points

Let points , , and be marked off some fixed distance along each of the sides , , and . Then the lines , , and concur in a point known as the first Yff point if

 (1)

This equation has a single real root , which can by obtained by solving the cubic equation

 (2)

where

 (3) (4) (5)

The isotomic conjugate is called the second Yff point. The triangle center functions of the first and second points are given by

 (6)

and

 (7)

respectively.

Analogous to the inequality for the Brocard angle , holds for the Yff points, with equality in the case of an equilateral triangle. Analogous to

 (8)

for , 2, 3, the Yff points satisfy

 (9)

Yff (1963) gives a number of other interesting properties. The line is perpendicular to the line containing the incenter and circumcenter , and its length is given by

 (10)

where is the area of the triangle.

The Cevian triangles of the Yff points are known as the Yff triangles.

Brocard Points, First Yff Triangle, Second Yff Triangle

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## References

Yff, P. "An Analog of the Brocard Points." Amer. Math. Monthly 70, 495-501, 1963.

Yff Points

## Cite this as:

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