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 (R - d)cos A - 2R cos B cos C : (R - d)cos B - 2R cos C cos A : (R - d)cos C - 2R cos A cos B,
where R = circumradius, d = distance |OH| between X(3) and X(4). (Joe Goggins, 2002)
Trilinears f(a,b,c) : f(b,c,a) : f(c,a,b),
where f(a,b,c) = (1 - J) cos A - 2 cos B cos C, where J = |OH|/R; explicitly,
J = (1/abc)[S(6) - S(2,4) + 3a2b2c2]1/2, where S(6) = a6 + b6 + c6, and
S(2,4) = a2b4 + a2c4 + b2c4 + b2a4 + c2a4 + c2b4 (Peter J. C. Moses, 10/2/03)
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
= g(a,b,c) : g(b,c,a) : g(c,a,b),
where g(a,b,c) = 2RSBSC + (|OH| - R)a2SA,
|OH| = distance between X(3) and X(4), and R = circumradius (Peter J. C. Moses, 3/2003; cf. X(1313), X(1314))
X(1113) is a point of intersection of the Euler line and the circumcircle. The other is X(1114). Of the two, X(1113) is the one closer to X(4).
X(1113) = trilinear product X(110)*X(1823).
X(1113) lies on these lines: 2,3 109,1822
X(1113) = midpoint of X(4) and X(1312)
X(1113) = reflection of X(I) in X(J) for these (I,J): (4,1312), (1114,3)
X(1113) = anticomplement of X(1313)
X(1113) = X(250)-Ceva conjugate of X(1114)