“Yff Points”的概念、定义、习题解题方法及翻译-数学辞典

单词

Yff Points

释义

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 Point

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 containingthe Incenter and Circumcenter , and its length is given by

(10)

where

is the Area of the Triangle.

See also Brocard Points, Yff Triangles

References

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

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