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 1/a2 : 1/b2 : 1/c2
= 1/(1 - cos 2A) : 1/(1 - cos 2B) : 1/(1 - cos 2C)Barycentrics 1/a : 1/b : 1/c
This is the center X(37) of the anticomplementary triangle.
X(75) lies on these lines:
1,86 2,37 6,239 7,8 9,190 10,76 19,27 21,272 31,82 32,746 38,310 43,872 48,336 77,664 99,261 100,675 101,767 141,334 144,391 158,240 194,1107 225,264 234,556 257,698 280,309 299,554 523,876 537,668 689,745 700,971 753,789 758,994 799,897 811,1099X(75) is the {X(7),X(8)}-harmonic conjugate of X(69).
X(75) = reflection of X(I) in X(J) for these (I,J): (192,37), (335,1086), (984,10)
X(75) = isogonal conjugate of X(31)
X(75) = isotomic conjugate of X(1)
X(75) = complement of X(192)
X(75) = anticomplement of X(37)
X(75) = X(I)-Ceva conjugate of X(J) for these (I,J): (76,312), (274,2), (310,76), (314,69)
X(75) = cevapoint of X(I) and X(J) for these (I,J): (1,63), (2,8), (7,347), (10,321), (244,514)X(75) = X(I)-cross conjugate of X(J) for these (I,J):
(1,92), (2,85), (7,309), (8,312), (10,2), (38,1), (63,304), (244,514), (307,69), (321,76), (347,322), (522,190)X(75) = crosspoint of X(I) and X(J) for these (I,J): (2,330), (274,310)
X(75) = crossdifference of any two points on line X(667)X(788)
X(75) = X(I)-Hirst inverse of X(J) for these (I,J): (2,350), (334,335)
X(75) = X(83)-aleph conjugate of X(31)X(75) = X(I)-beth conjugate of X(J) for these (I,J):
(8,984), (75,7), (99,77), (314,75), (522,876), (645,9), (646,75), (668,75), (811,342)