## X(647) (CROSSDIFFERENCE OF X(2) AND X(3))

 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) = a(b2 - c2)(b2 + c2 - a2)
= u(A,B,C) : u(B,C,A) : u(C,A,B), where u(A,B,C) = sin 2A sin(B - C)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(647) = point whose trilinears are coefficients for the Euler line.
X(647) = radical center of the circumcircle, nine-point center, and Brocard circle (Wilson Stothers, 3/13/2003)

X(647) lies on these lines: 1,1021    2,850    50,654    111,842    184,878    187,237    230,231    441,525    520,652

X(647) = isogonal conjugate of X(648)
X(647) = complement of X(850)
X(647) = X(I)-Ceva conjugate of X(J) for these (I,J): (2,125), (107,51), (110,184), (112,6), (1304,1495)
X(647) = crosspoint of X(I) and X(J) for these (I,J): (2,110), (6,112), (107,275)

X(647) = crosssum of X(I) and X(J) for these (I,J): (1,1021), (2,525), (6,523), (110,112), (185,647), (216,520), (512,1196), (651,653), (850,1235)

X(647) = crossdifference of any two points on line X(2)X(3)
X(647) = orthojoin of X(125)

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