## X(1127) (1ST DE VILLIERS POINT)

 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) = (sin A/4)/sin(3A/4)
Trilinears           gA,B,C) : g(B,C,A) : g(C,A,B),
where g(A,B,C) = [1 - 2 cos(A/2)]/(1 + 2 cos A)       (M. Iliev, 5/13/07)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Let A', B', C' be the incenters of triangles XBC, XCA, XAB, respectively, where X is the incenter, X(1). The triangle A'B'C' is perspective to ABC, and the perspector is X(1127). Coordinates found by Darij Grinberg, 8/22/02.

Michael de Villiers, A dual to Kosnita's theorem, reprinted from Mathematics & Informatics Quarterly 6 (1996) 1996.

X(1127) lies on this line: 174,481

X(1127) = isogonal conjugate of X(1129)

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