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Trisected perimeter point

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Trisected perimeter point

In geometry, given a triangle ABC, there exist unique points A´, B´, and C´ on the sides BC, CA, AB respectively, such that:

  • A´, B´, and C´ partition the perimeter of the triangle into three equal-length pieces. That is,
  • The three lines AA´, BB´, and CC´ meet in a point, the trisected perimeter point.

    • This is point X369 in Clark Kimberling's Encyclopedia of Triangle Centers. Uniqueness and a formula for the trilinear coordinates of X369 were shown by Peter Yff late in the twentieth century. The formula involves the unique real root of a cubic equation.

    References

    Trisected perimeter point Wikipedia
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