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(b + c - 2a)[2abc - (b + c)(a2 - (b - c)2)]
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
Let A',B',C' be the respective excenters of ABC, and let Ab be the projection of A on A'B', let Ac be the projection of A on A'C', and define Bc, Ba, Ca, Cb cyclically. The Euler lines of the three triangles A'AbAc, B'BcBa, C'CaCb concur in X(1145). Also, X(1145) is X(974) of the excentral triangle. (Analogously, X(442) is X(973) of the excentral triangle; see the note at X(442).) Jean-Pierre Ehrmann (#4200, 10/24/01)
X(1145) lies on these lines:
2,1000 3,8 9,80 10,11 119,517 144,153 214,519 484,529
X(1145) = midpoint of X(8) and X(100)
X(1145) = reflection of X(I) in X(J) for these (I,J): (11,10), (1317,214), (1320,1387), (1537,119)
X(1145) = anticomplement of X(1387)