## X(405) (EULER LINE INTERCEPT OF LINE X(1)X(6))

 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) = bc(a + b + c) + abc cos A
Barycentrics    b + c + a(1 + cos A) : c + a + b(1 + cos B) : a + b + c(1 + cos C)

X(405) lies on these lines: 1,6    2,3    8,943    10,55    56,226    58,940    63,942    284,965    329,999    756,976    846,986

X(405) is the {X(2),X(3)}-harmonic conjugate of X(474). For a list of harmonic conjugates of X(405), click More at the top of this page.

X(405) = inverse-in-orthocentroidal circle of X(442)
X(405) = complement of X(377)
X(405) = crosssum of X(838) and X(1015)
X(405) = crossdifference of any two points on line X(513)X(647)

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