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) = bc[3a4 - 2a3(b + c) + (b - c)2(2ab + 2ac - 2bc - b2 - c2 - 2a2)]
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = 1 - cos A - cos B - cos C + cos B cos C
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
X(944) is the point in which the extended legs X(4)X(1) and X(3)X(8) of the trapezoid X(4)X(1)X(3)X(8) meet. The point is introduced in
Hofstadter, Douglas. R., "Discovery and dissection of a geometric gem," in Geometry Turned On! editors J. R. King and D. Schattschneider, Mathematical Association of America, Washington, D. C., 1997, 3-14.
The centroid of ABC is also the centroid of triangle X(4)X(8)X(944). (Darij Grinberg, August 22, 2002)
X(944) lies on these lines:
1,4 2,355 3,8 10,631 20,145 30,962 40,376 48,281 80,499 84,1000 150,348 390,971 392,452 938,999 958,1006
X(944) = midpoint of X(20) and X(145)
X(944) = reflection of X(I) in X(J) for these (I,J): (4,1), (8,3), (355,1385), (962,1482)
X(944) = isogonal conjugate of X(945)
X(944) = anticomplement of X(355)