There exist points A', B', and C' on segments B C, C A, and A B of a triangle, respectively, such that A' C + C B' = B' A + A C' = C' B + B A' and the lines A A', B B', C C' concur. The point of concurrence is called the trisected perimeters point, which is Kimberling center X_369. Near the end of the 20th century, P.

Cevian | perimeter | semiperimeter | trisection