## X(1981) (VEGA TRANSFORM OF X(647))

 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 2B sin(C - A) - sin 2C sin(A - B)]/[sin 2A sin(B - C)]
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

If X = x : y : z is a triangle center other than X(1), then the Vega transform of X, defined by trilinears

(y - z)/x : (z - x)/y : (x - y)/z

lies on the line [x:y:z] that has x,y,z as coefficients. (The line [x:y:z] is the trilinear polar of the isogonal conjugate of X.) Thus, the Vega transform of X(647) lies on the Euler line.

In general, the bicentrics of X also lie on [x:y:z]; for details, click More at the top of this page.

X(1981) lies on these lines: 2,3    651,653    662,811

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