Trilinears           a/(a - L) : b/(b - L) : c/(c - L),
                                    where L = L(a,b,c) is the smallest root of a²/(a - L) + b²/(b - L) + c²/(c - L) = 2D/L
                                    where D = area(ABC).
Barycentrics    a²/(a - L) : b²/(b - L) : c²/(c - L)

Suppose P is a point inside triangle ABC. Let S_a be the square inscribed in triangle PBC, having two vertices on segment BC, one on PB, and one on PC. Define S_b and S_c cyclically. Then X(1144) is the unique choice of P for which the three squares are congruent. The function L(a,b,c) is symmetric, homogeneous of degree 1, and satisfies 0 < L(a,b,c) < min{a,b,c}. Also, X(1144) lies on the hyperbola {A,B,C,X(1),X(6)}; indeed, X(1144) lies on the open arc from X(1) to the vertex of ABC opposite the shortest side. L(a,b,c) is the common length of the sides of the three squares. (Jean-Pierre Ehrmann, 12/16/01)