Interactive Applet |
You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.
You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon _{}, select the center name from the list and, then, click on the vertices A, B and C successively.
Information from Kimberling's Encyclopedia of Triangle Centers |
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = (cos A)[cos^{2}B + cos^{2}C - cos^{2}A]
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)