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:

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.