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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 X<sub>369</sub> in Clark Kimberling's Encyclopedia of Triangle Centers. Uniqueness and a formula for the trilinear coordinates of X<sub>369</sub> were shown by Peter Yff late in the twentieth century. The formula involves the unique real root of a cubic equation.

See also

References