## X(2491) (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, GALLATLY CIRCLE})

 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) = a3(b2 - c2)(b4 + c4 - a2b2 - a2c2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2491) lies on these lines:
39,690    230,231    351,865    512,2021    669,688    804,2023    882,2422

X(2491) = X(I)-Ceva conjugate of X(J) for these I,J: 882,688    2395,512    2396,511
X(2491) = crosspoint of X(I) and X(J) for these I,J: 2,805    112,1976    511,2396    512,2395    669,881
X(2491) = crosssum of X(I) and X(J) for these I,J: 6,804    98,2422    99,2421    325,525    645,874    670,880

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