Trisected perimeter point
[Image:Trisected perimeter point 3-4-5.svg|thumb|240px|The trisected perimeter point of a 3-4-5 right triangle. For this triangle, and, but that is not the case for triangles of other shapes.]
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.