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 f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = a[b2cos 2B + c2cos 2C - a2cos 2A]
Trilinears g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (J2 - 3) cos A + 4 cos B cos C, where J is as at X(1113)Barycentrics h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = a2(b2cos 2B + c2cos 2C - a2cos 2A)
Theorems involving X(26), published in 1889 by A. Gob, are discussed in
Roger A. Johnson, Advanced Euclidean Geometry, Dover, 1960, 259-260.
X(26) lies on these lines: 2,3 6,143 52,184 68,161 98,1286 154,155 206,511 1605,1607 1606,1608
X(26) is the {X(154),X(155)}-harmonic conjugate of X(156).
X(26) = reflection of X(155) in X(156)
X(26) = isogonal conjugate of X(70)
X(26) = inverse-in-circumcircle of X(2072)
X(26) = crosssum of X(125) and X(924)