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) = a2(b + c)2 + a(b + c)(b2 + c2)
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
Let A' be the point common to Apollonius circle and the A-excircle, and define B' and C' cyclically. Then triangle A'B'C' is perspective to the cevian triangle of X(6), and the perspector is X(2092). (Eric Danneels, Hyacinthos, #8070, 10/01/03). (Triangle A'B'C' is also perspective to the cevian triangle of X(1); see X(1682).)
X(2092) lies on these lines: 2,314 3,6 9,43 10,37 42,181 69,980 71,213 115,119 214,1015 232,1172 407,1880 442,1738 1193,1682
X(2092) = midpoint of X(I) and X(J) for these (I,J): (256,1045), (2019,2020)
X(2092) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,960), (100,512), (1415,647)
X(2092) = crosspoint of X(I) and X(J) for these (I,J): (2,65), (6,37), (429,1211)
X(2092) = crosssum of X(I) and X(J) for these (I,J): (2,81), (6,21), (58,572), (1169,1798)