## X(2420) (ISOGONAL CONJUGATE OF X(2394))

 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            1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b), where f(a,b,c) is as given just before X(2394)
Barycentrics    a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)

Centers X(2420) to X(2445), on the cubic K162, are isogonal conjugates of centers X(2394) to X(2419), which are on the Simson cubic, K010. For details, see the note just before X(2394).

X(2420) lies on the cubic K162 and these lines:
3,6    110,112    249,2421    691,2422    2433,2437

X(2420) = isogonal conjugate of X(2394)
X(2420) = crosspoint of X(476) and X(648)
X(2420) = crosssum of X(I) and X(J) for these I,J: 523,1637    526,647

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