## X(2090) (1ST STEVANOVIC PERSPECTOR)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

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 B/2 + sin C/2) csc A
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Let A' be the point in which the angle bisector AX(1) meets the A-excircle of triangle ABC, and define B' and C' cyclically. Then triangle A'B'C' is perspective to the medial triangle, and the perspector is X(2090). (Milorad Stevanovic, Hyacinthos #8088, 10/02/03)

X(2090) lies on these lines: 2,174    8,188    9,362    85,555    92,2091    177,178    312,556

X(2090) = complement of X(174)
X(2090) = crosspoint of X(2) and X(556)

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