Interactive Applet |
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) = 1/(cos B + cos C - cos A - 1)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)Let A',B',C' be the excenters. The perpendiculars from B' to AB and from C' to AC meet in a point A". Points B" and C" are determined cyclically. The hexyl triangle, A"B"C", is perspective to ABC, and X(84) is the perspector.
X(84) lies on these lines: 1,221 3,9 4,57 7,946 8,20 21,285 33,603 36,90 46,80 58,990 171,989 256,988 294,580 309,314 581,941 944,1000
X(84) = reflection of X(I) in X(J) for these (I,J): (40,1158), (1490,3)
X(84) = isogonal conjugate of X(40)
X(84) = isotomic conjugate of X(322)
X(84) = X(I)-Ceva conjugate of X(J) for these (I,J): (189,282), (280,1)
X(84) = X(I)-cross conjugate of X(J) for these (I,J): (19,57), (56,1)
X(84) = X(280)-aleph conjugate of X(84)
X(84) = X(I)-beth conjugate of X(J) for these (I,J): (271,3), (280,280), (285,84)