## X(1691) (RADICAL TRACE OF CIRCUMCIRCLE AND 1ST LEMOINE CIRCLE)

 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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Download all construction files and macros: tc.zip (10.1 Mb).
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(A - 2ω)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

X(1691) lies on these lines:
2,1501    3,6    31,893    83,316    98,230    99,698    141,1078    154,1611    184,1613    237,694    249,524    385,732    691,729    695,1176    699,805    1428,1914    1968,1974

X(1691) = midpoint of X(I) and X(J) for these (I,J): (6,2076), (187,1692), (1687,1688)
X(1691) = reflection of X(I) in X(J) for these (I,J): (6,1692), (2076,187)
X(1691) = isogonal conjugate of X(1916)
X(1691) = inverse-in-circumcircle of X(32)
X(1691) = inverse-in-Brocard circle of X(3094)
X(1691) = inverse-in-1st-Lemoine-circle of X(6)
X(1691) = inverse-in-2nd-Lemoine-circle of X(576)
X(1691) = X(I)-Ceva conjugate of X(J) for these (I,J): (237,1971), (699,32), (1976,6)
X(1691) = crosspoint of X(I) and X(J) for these (I,J): (83,98), (385,419)
X(1691) = crosssum of X(39) and X(511)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense