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) = sin B sin C [(sin C)/(cos C - 2 cos A cos B) + (sin B)/(cos B - 2 cos A cos C)]
Barycentrics g(A,B,C) : g(B,C,A) : g(C,A,B), where
g(A,B,C) = (sin C)/(cos C - 2 cos A cos B) + (sin B)/(cos B - 2 cos A cos C)
= h(a,b,c) : h(b,c,a) : h(c,a,b),
where h(a,b,c) = b2/(b2SB - 2SASC) + c2/(c2SC - 2SASB),
SA = (b2 + c2 - a2)/2, and SB and SC are defined cyclically (Peter J. C. Moses, 3/2003)
X(113) = nine-point-circle-antipode of of X(125)
X(113) = X(74)-of-medial triangle
X(113) = X(104)-of-orthic triangle
X(113) lies on these lines:
2,74 3,122 4,110 5,125 6,13 11,942 52,135 114,690 123,960 127,141 137,546
X(113) = midpoint of X(I) and X(J) for these (I,J): (4,110), (74,146), (265,399)
X(113) = reflection of X(I) in X(J) for these (I,J): (52,1112), (125,5)
X(113) = complementary conjugate of X(30)
X(113) = X(4)-Ceva conjugate of X(30)
X(113) = crosspoint of X(4) and X(403)
X(113) = crossdifference of any two points on line X(526)X(686)