## X(484) (1ST EVANS 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           1 + 2(cos A - cos B - cos C) : 1 + 2(cos B - cos C - cos A) : 1 + 2(cos C - cos A - cos B)
Barycentrics    a[1 + 2(cos A - cos B - cos C)] : b[1 + 2(cos B - cos C - cos A)] : c[1 + 2(cos C - cos A - cos B)]

X(484) is the perspector of the excentral triangle and the triangle A'B'C', where A' is the reflection of vertex A in sideline BC and B', C' are determined cyclically. (Lawrence Evans, 10/22/98)

X(484) lies on these lines: 1,3    10,191    12,79    30,80    63,535    100,758    499,962    759,901    1046,1048

X(484) = reflection of X(I) in X(J) for these (I,J): (1,36), (36,1155)
X(484) = inverse-in-circumcircle of X(35)
X(484) = inverse-in-Bevan-circle of X(1)
X(484) = isogonal conjugate of X(3065)
X(484) = X(80)-Ceva conjugate of X(1)
X(484) = crossdifference of any two points on line X(650)X(1100)

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