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 csc 2A : csc 2B : csc 2C
Barycentrics sec A : sec B : sec CLet LA be the line through X(4) parallel to the internal bisector of angle A, and let
A' = BC∩LA. Define B' and C' cyclically.Alexei Myakishev, "The M-Configuration of a Triangle," Forum Geometricorum 3 (2003) 135-144,
proves that the lines AA', BB', CC' concur in X(92). He notes that another construction follows from Proposition 2 of the article: let A1 be the midpoint of the arc BC of the circumcircle that passes through A, and let A2 be the point, other than A, in which the A-altitude meets the circumcircle. Let A" = A1A2∩BC. Define B" and C" cyclically. Then the lines AA", BB", CC" concur in X(92).
X(92) lies on these lines:
1,29 2,273 4,8 7,189 19,27 25,242 31,162 38,240 40,412 47,91 55,243 57,653 85,331 100,917 226,342 239,607 255,1087 257,297 264,306 304,561 406,1068 608,894X(92) = isogonal conjugate of X(48)
X(92) = isotomic conjugate of X(63)
X(92) = anticomplement of X(1214)
X(92) = X(I)-Ceva conjugate of X(J) for these (I,J): (85,342), (264,318), (286,4), (331,273)
X(92) = cevapoint of X(I) and X(J) for these (I,J): (1,19), (4,281), (47,48), (196,278)
X(92) = X(I)-cross conjugate of X(J) for these (I,J): (1,75), (4,273), (19,158), (48,91), (226,2), (281,318)
X(92) = crosspoint of X(I) and X(J) for these (I,J): (85,309), (264,331)
X(92) = crossdifference of any two points on line X(810)X(822)
X(92) = X(275)-aleph conjugate of X(47)
X(92) = X(I)-beth conjugate of X(J) for these (I,J): (92,278), (312,329), (648,57)