## X(2967) (1ST 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) = (a2cos B cos C - bc cos2A)2(sec A)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2967) lies on these lines:
2,1972    3,112    4,147    5,339    25,110    98,648    114,132    186,2080    232,511    250,842    262,264    324,427    1312,2592    1313,2593

X(2967) = reflection of X(339) in X(5)
X(2967) = X(274)-Ceva conjugate of X(297)
X(2967) = crosspoint of X(264) and X(297)
X(2967) = crosssum of X(I) and X(J) for these I,J: 125,879    184,248

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