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/(cos B - cos C) : b/(cos C - cos A): c/(cos A - cos B)
= g(a,b,c) : g(b,c,a) : g(c,a,b) where g(a,b,c) = a/[(b - c)(b + c - a)]Barycentrics a2/(cos B - cos C) : b2/(cos C - cos A): c2/(cos A - cos B)
X(109) = circumcircle-antipode of X(102)
X(109) = Λ(X(1), X(3))
X(109) = trilinear product X(1381)*X(1382)
X(109) lies on these lines:
1,104 2,124 3,102 4,117 7,675 20,151 31,57 34,46 35,73 36,953 40,255 55,103 56,106 58,65 59,901 85,767 98,171 99,643 100,651 101,654 107,162 108,1020 112,163 165,212 191,201 278,917 284,296 478,573 579,608 604,739 649,919 658,927 662,931 840,902X(109) = midpoint of X(20) and X(151)
X(109) = reflection of X(I) in X(J) for these (I,J): (4,117), (102,3)
X(109) = isogonal conjugate of X(522)
X(109) = anticomplement of X(124)
X(109) = X(I)-Ceva conjugate of X(J) for these (I,J): (59,56), (162,108)
X(109) = cevapoint of X(65) and X(513)
X(109) = X(I)-cross conjugate of X(J) for these (I,J): (56,59), (513,58)
X(109) = crosspoint of X(110) and X(162)
X(109) = crosssum of X(I) and X(J) for these (I,J): (523,656), (652,663)
X(109) = crossdifference of any two points on line X(11)X(1146)
X(109) = X(I)-aleph conjugate of X(J) for these (I,J): (100,1079), (162,580), (651,223)
X(109) = X(I)-beth conjugate of X(J) for these (I,J): (21,104), (59,109), (100,100), (110,109), (765,109), (901,109)
X(109) = trilinear product of X(1381) and X(1382)