## X(2023) (RADICAL TRACE OF GALLATLY AND NINE-POINT CIRCLES)

 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 ω cos(B - C) - cos 2ω sin(A + ω)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(2023) lies on these lines:
2,6943,6    5,39    6,98    30,2021    194,1007    230,511    325,732    625,736    1503,2024    1575,1738

X(2023) = midpoint of X(39) and X(115)
X(2023) = crosssum of X(1662) and X(1663)

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