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) = 5 cos A - 4 cos B cos C - 8 sin B sin C cos2A
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,B,A)
Let L, M, N be lines through A, B, C, respectively, parallel to the Euler line. Let L' be the reflection of L in sideline BC, let M' be the reflection of M in sideline CA, and let N' be the reflection of N in sideline AB. The lines L', M', N' concur in X(399).
Cyril Parry, Problem 10637, American Mathematical Monthly 105 (1998) 68.
X(399) lies on these lines:
3,74 4,195 6,13 30,146 155,382 394,541
X(399) = isogonal conjugate of X(1138)
X(399) = reflection of X(I) in X(J) for these (I,J): (3,110), (74,1511), (265,113)
X(399) = X(I)-Ceva conjugate of X(J) for these (I,J): (30,3), (323,6)