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 a(2a2 - b2 - c2) : b(2b2 - c2 - a2) : c(2c2 - a2 - b2)
=sin A - 3 cos A tan ω : sin B - 3 cos B tan ω : sin C - 3 cos C tan ω (Peter J. C. Moses, 8/22/03)Barycentrics a2(2a2 - b2 - c2) : b2(2b2 - c2 - a2) : c2(2c2 - a2 - b2)
X(187) lies on these lines:
2,316 3,6 23,111 30,115 35,172 36,1015 74,248 99,385 110,352 112,186 183,1003 237,351 249,323 325,620 395,531 396,530 729,805X(187) is the {X(3),X(6)}-harmonic conjugate of X(574).
X(187) is the radical trace of the circumcircle and Brocard circle. (Peter J. C. Moses, 8/24/03)
X(187) = midpoint of X(I) and X(J) for these (I,J): (15,16), (99,385)
X(187) = reflection of X(I) in X(J) for these (I,J): (115,230), (316,625), (325,620)
X(187) = isogonal conjugate of X(671)
X(187) = inverse-in-circumcircle of X(6)
X(187) = inverse-in-Brocard-circle of X(574)
X(187) = complement of X(316)
X(187) = anticomplement of X(625)
X(187) = X(111)-Ceva conjugate of X(6)
X(187) = crosspoint of X(I) and X(J) for these (I,J): (2,67), (6,111), (468,524)
X(187) = crosssum of X(I) and X(J) for these (I,J): (2,524), (6,23), (111,895), (115,690)
X(187) = crossdifference of any two points on line X(2)X(523)
X(187) = X(55)-beth conjugate of X(187)