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) = 3 cos(B - C) - 2 cos A,
= cos A + 6 cos B cos C : cos B + 6 cos C cos A : cos C + 6 cos A cos B
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
X(546) lies on the Euler line. (Antreas Hatzipolakis, 1/20/00, Hyacinthos #201)
Let MA denote the point in which the A-median meets side BC. On 11/05/03, Andrew Crane noted that X(546) is the radical center of circles (A), (B), (C), where (A) denotes the circle centered at A and passing through MA, and (B) and (C) are defined cyclically.
X(546) lies on these lines: 2,3 13,398 14,397 113,137 156,578 946,952
X(546) = midpoint of X(I) and X(J) for these (I,J): (4,5), (382,550)
X(546) = reflection of X(I) in X(J) for these (I,J): (140,5), (548,140)
X(546) = inverse-in-orthocentroidal-circle of X(382)
X(546) = complement of X(550)