## X(2493) (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, PARRY CIRCLE})

 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) = a[a6(b2 + c2) - a4(b2 + c2)2 + (b4 - b2c2 + c4)((b2 - c2)2 - T)],
where T = a2(b6 - 2b4c2 - 2b2c4 + c6)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2493) lies on these lines:
2,94    5,39    6,110    23,50    24,112    25,1576    53,136    230,231    1084,1196

X(2493) = crosspoint of X(2) and X(842)
X(2493) = crosssum of X(6) and X(542)

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