## X(2489) (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE 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(b2 - c2)/(b2 + c2 - a2)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(2489) lies on these lines:
6,924    19,876    112,250    230,231    393,2395    512,1692    520,2451    882,1843    1974,2422    2507,2524

X(2489) = reflection of X(I) in X(J) for these I,J: 647,2485    2485,2492    2524,2507
X(2489) = X(112)-Ceva conjugate of X(25)
X(2489) = cevapoint of X(647) and X(2519)
X(2489) = X(I)-cross conjugate of X(J) for these I,J: 669,512    1084,1974
X(2489) = crosspoint of X(25) and X(112)

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