Trilinears           f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (cos A)[cos²B + cos²C - cos²A]
Barycentrics    g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = (sin A)f(A,B,C)

X(4) of the tangential triangle. This point is also the center of the circle which cuts (extended) lines BC, CA, AB in pairs of points A' and A", B' and B", C' and C", respectively, such that angles A'AA", B'BB", C'CC" are all right angles. This is the Dou circle, described in

Jordi Dou, Problem 1140, Crux Mathematicorum, 28 (2002) 461-462.

X(155) lies on these lines:

1,90    3,49    4,254    5,6    20,323    24,110    25,52    26,154    30,1498    159,511    195,381    382,399    450,1075    648,1093    651,1068

X(155) is the {X(26),X(156)}-harmonic conjugate of X(154). For a list of harmonic conjugates of X(155), click More at the top of this page.

X(155) = reflection of X(I) in X(J) for these (I,J): (3,1147), (26,156), (68,5)
X(155) = isogonal conjugate of X(254)
X(155) = eigencenter of cevian triangle of X(4)
X(155) = eigencenter of anticevian triangle of X(3)
X(155) = X(4)-Ceva conjugate of X(3)
X(155) = crosssum of X(136) and X(523)