## X(2972) (6th MACBEATH POINT)

 Interactive Applet

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.

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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) = [bc(b2 - c2)]2cos3A
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2972) lies on these lines:
2,1972    3,74    25,1073    69,1942    122,125    127,136    394,426    511,852    1368,2974    1624,2781

X(2972) = X(I)-Ceva conjugate of X(J) for these I,J: 3,520    264,525    1073,647
X(2972) = crosspoint of X(I) and X(J) for these I,J: 3,520    64,523    264,525
X(2972) = crosssum of X(I) and X(J) for these I,J: 4,107    20,110    112,184

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