Yff triangles

Let points A', B', and C' be marked off some fixed distance x along each of the sides B C, C A, and A B. Then the lines A A', B B', and C C' concur in a point U known as the first Yff point if x^3 = (a - x)(b - x)(c - x). This equation has a single real root u, which can by obtained by solving the cubic equation f(x) = 2x^3 - p x^2 + q x - r = 0, where p | = | a + b + c q | = | a b + a c + b c r | = | a b c.

Brocard points | first Yff triangle | second Yff triangle