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[a4(b2 + c2) - 2a2(b4 + c4) + b6 + c6 ]/(b2 + c2 - a2)
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)
X(1112) is the center of the conic that passes through the vertices of the cevian triangles of X(4) and X(648), and also through the centers X(I) for I = 4, 113, 155, 193. (Paul Yiu, Oct. 16, 2001, as contributing editor for "Conics associated with a cevian nest," Forum Geometricorum 1 (2001) 141-150; see Example 2.)
X(1112) lies on these lines:
4,94 25,110 51,125 52,113 389,974 428,542 468,511
X(1112) = reflection of X(974) in X(389)
X(1112) = crosspoint of X(4) and X(250)
X(1112) = crosssum of X(3) and X(125)