## X(1112) (CROSSPOINT OF X(4) AND X(250))

 Interactive Applet

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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[a4(b2 + c2) - 2a2(b4 + c4) + b6 + c6 ]/(b2 + c2 - a2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(1112) is the center of the conic that passes through the vertices of the cevian triangles of X(4) and X(648), and also through the centers X(I) for I = 4, 113, 155, 193. (Paul Yiu, Oct. 16, 2001, as contributing editor for "Conics associated with a cevian nest," Forum Geometricorum 1 (2001) 141-150; see Example 2.)

X(1112) lies on these lines:
4,94    25,110    51,125    52,113    389,974    428,542    468,511

X(1112) = reflection of X(974) in X(389)
X(1112) = crosspoint of X(4) and X(250)
X(1112) = crosssum of X(3) and X(125)

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