## X(1321) (1ST YIU SQUARES PERSPECTOR)

 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) = (2 cos A + sin A)/(cos2A + cos A sin A)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Let BBaCa be the external square on side BC, and define CCbAbA and AAcBcB cyclically. Let X = BCb∩CBc and X' = BAb∩CAc, and define Y, Z and Y', Z' cyclically. The lines AX, BY, CZ concur in X(4), and the lines AX', BY', CZ' concur in X(485). The lines XX', YY', ZZ' concur in X(1321), as shown in

X(1321) lies on this line: 4,371

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