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 cos A - cos 2A cos(B - C) : cos B - cos 2B cos(C - A) : cos C - cos 2C cos(A - B)
Barycentrics a[cos A - cos 2A cos(B - C)] : b[cos B - cos 2B cos(C - A)] : c[cos C - cos 2C cos(A - B)]
If ABC is acute then X(389) is the Spieker center of the orthic triangle. Peter Yff reports (Sept. 19, 2001) that since X(389) is on the Brocard axis, there must exist T for which X(389) is sin(A+T) : sin(B+T) : sin(C+T), and that tan(T) = - cot A cot B cot C.
X(389) lies on these lines:
3,6 4,51 24,184 30,143 54,186 115,129 217,232 517,950
X(389) = midpoint of X(I) and X(J) for these (I,J): (3,52), (4,185), (974,1112)
X(389) = reflection of X(1216) in X(140)
X(389) = inverse-in-Brocard-circle of X(578)
X(389) = crosspoint of X(4) and X(54)
X(389) = crosssum of X(I) and X(J) for these (I,J): (3,5), (6,418)