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) = a cos A - (b + c)cos(B - C)
Trilinears g(a,b,c) : g(b,c,a) : g(c,a,b),
where g(a,b,c) = bc(b + c)[a2(b2 + c2) - (b2 - c2)2] - a3bc(b2 + c2 - a2) (Michel Garitte, 4/3/03)
Barycentrics af(a,b,c) : bf(b,c,a) : cf(c,a,b)
X(355) = the center of the Fuhrmann circle, defined as the circumcircle of the Fuhrmann triangle A"B"C", where A" is obtained as follows: let A' be the midpoint of the shorter arc having endpoints B and C on the circumcircle of ABC; then A" is the reflection of A' in line BC. Vertices B" and C" are obtained cyclically.
Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, 1995. Chapter 6: The Fuhrmann Circle.
X(355) lies on these lines:
1,5 2,944 3,10 4,8 30,40 65,68 85,150 104,404 165,550 381,519 382,516 388,942 938,1056
X(355) = midpoint of X(4) and X(8)
X(355) = reflection of X(I) in X(J) for these (I,J): (1,5), (3,10), (944,1385), (1482,946)
X(355) = anticomplement of X(1385)
X(355) = complement of X(944)