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) = bc(b - c)2
Barycentrics g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = (b - c)2
The line f(a,b,c)x + f(b,c,a)y + f(c,a,b)z = 0 is tangent to the circumcircle at X(101). Also, X(1086) is the point of tangency of the Steiner inscribed ellipse with the line tangent to the nine-point circle and the incircle. (Paul Yiu, #4197, 11/24/01).
X(1086) lies on these lines:
1,528 2,45 6,7 8,599 10,537 11,244 37,142 44,527 53,273 57,1020 75,141 115,116 220,277 239,320 812,1015 918,1111
X(1086) = midpoint of X(I) and X(J) for these (I,J): (2,903), (7,673), (75,335), (239,320)
X(1086) = isogonal conjugate of X(1252)
X(1086) = isotomic conjugate of X(1016)
X(1086) = complement of X(190)
X(1086) = crosspoint of X(2) and X(514)
X(1086) = crosssum of X(I) and X(J) for these (I,J): (6,101), (9,1018), (32,692), (219,906)
X(1086) = crossdifference of any two points on line X(101)X(692)