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 bcf(a,b,c) : caf(b,c,a): abf(c,a,b), where f(a,b,c) is the 1st barycentric given below
Barycentrics f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = [d2 + (4r - R)R + sqrt(Q)]SBSC + (d2 + 2r2 - R2)a2SA,
where Q = 4d2R(4r - R) + [d2 - 3R2 + 4r(r + R)]2,
d = distance between X(3) and X(4),
R = circumradius, r = inradius,
SA = (b2 + c2 - a2)/2, and SB and SC are defined cyclically (Peter J. C. Moses, 3/2003)
X(1314) is a point of intersection of the Euler line and the incircle. For some obtuse triangles, this point is not in the real plane (specifically, for those a,b,c such that Q < 0).
X(1314) lies on this line: 2,3
X(1314) lies on the incircle