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) = 1/[a(b2 - c2)(b2 + c2 - a2)]
= u(A,B,C) : u(B,C,A) : u(C,A,B), where u(A,B,C) = csc 2A csc(B - C)
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)X(648) is constructed as the pole of the Euler line L as follows: let A", B", C" be the points where L meets the sidelines BC, CA, AB of the reference triangle ABC. Let A', B', C' be the harmonic conjugates of A", B", C" with respect to {B,C}, {C,A}, {A,B}, respectively, The lines AA', BB', CC' concur in X(648).
X(648) lies on these lines:
4,452 6,264 27,903 94,275 95,216 99,112 107,110 108,931 132,147 155,1093 162,190 185,1105 193,317 232,385 249,687 250,523 297,340 447,519 645,668 651,823 653,662 925,933 1020,1021 1075,1092X(648) = reflection of X(I) in X(J) for these (I,J): (287,6), (340,297), (1494,2)
X(648) = isogonal conjugate of X(647)
X(648) = isotomic conjugate of X(525)
X(648) = cevapoint of X(110) and X(112)
X(648) = X(I)-cross conjugate of X(J) for these (I,J): (6,250), (110,99), (112,107), (520,95), (523,264)