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) = (sec2A/2)(2 cos2A/2 - cos2B/2 - cos2C/2)
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
= g(a,b,c) : g(b,c,a) : g(c,a,b),
where g(a,b,c) = (2a2 - b2 - c2 - ab - ac + 2bc)/(b + c - a) [P. J. C. Moses, 6/25/04]
X(1323) is the point of intersection of the line X(1)X(7) and the trilinear polar of X(7). These two lines are orthogonal.
X(1323) is named in honor of T. J. Fletcher in
Adrian Oldknow, "The Euler-Gergonne-Soddy Triangle of a Triangle," American Mathematical Monthly 103 (1996) 319-329.
MathWorld, Fletcher Point
X(1323) lies on these lines:
1,7 10,348 36,934 40,738 85,1125 106,927 165,479 241,514 519,664 1319,1355
X(1323) = inverse-in-incircle of X(7)
X(1323) = X(1260)-cross conjugate of X(527)
X(1323) = crossdifference of any two points on line X(55)X(657)