X(404) ({X(2),X(3)}-HARMONIC CONJUGATE OF X(21))

 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) - a(b2 + c2 - a2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = abc(a + b + c) - a2(b2 + c2 - a2)

X(404) lies on these lines:
1,88    2,3    8,56    10,36    31,978    46,997    57,78    60,662    63,936    69,1014    81,386    104,355    108,318    145,999    149,496    603,651    612,988    976,982

X(404) is the {X(2),X(3)}-harmonic conjugate of X(21). For a list of harmonic conjugates of X(404), click More at the top of this page.

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