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 a3 : b3 : c3
= sin(A - ω) : sin(B - ω) : sin(C - ω)
= sin A + sin(A - 2ω) : sin B + sin(B - 2ω) : sin C + sin(C - 2ω)
= cos A - cos(A - 2ω) : cos B - cos(B - 2ω) : cos C - cos(C - 2ω) (cf., X(39))Barycentrics a4 : b4 : c4
X(32) lies on these lines:
1,172 2,83 3,6 4,98 5,230 9,987 21,981 24,232 31,41 56,1015 75,746 76,384 81,980 99,194 100,713 101,595 110,729 163,849 184,211 218,906 512,878 538,1003 561,724 590,640 604,1106 615,639 731,825 733,827 910,1104 993,1107X(32) is the {X(3),X(6)}-harmonic conjugate of X(39).
X(32) = midpoint of X(371) and X(372)
X(32) = reflection of X(315) in X(626)
X(32) = isogonal conjugate of X(76)
X(32) = isotomic conjugate of X(1502)
X(32) = inverse-in-circumcircle of X(1691)
X(32) = inverse-in-Brocard-circle of X(39)
X(32) = inverse-in-1st-Lemoine-circle of X(1692)
X(32) = complement of X(315)
X(32) = anticomplement of X(626)
X(32) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,206), (6,184), (112,512), (251,6)
X(32) = crosspoint of X(I) and X(J) for these (I,J): (2,66), (6,25)X(32) = crosssum of X(I) and X(J) for these (I,J): (2,69), (6,22), (75,312), (115,826), (311,343), (313,321), (338,850), (339,525), (349,1231), (693,1086), (1229,1233), (1230,1269)
X(32) = crossdifference of any two points on line X(325)X(523)
X(32) = X(184)-Hirst inverse of X(237)
X(32) = X(I)-beth conjugate of X(J) for these (I,J): (41,41), (163,56), (919,32)
X(32) = external center of similitude of circumcircle and Moses circle