## X(1323) (FLETCHER POINT)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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.

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 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)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.