X(86) (CEVAPOINT OF INCENTER AND CENTROID)

 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           bc/(b + c) : ca/(c + a) : ab/(a + b)
Barycentrics    1/(b + c) : 1/(c + a) : 1/(a + b)

X(86) lies on these lines:
1,75    2,6    7,21    10,319    29,34    37,190    58,238    60,272    99,106    110,675    142,284    239,1100    269,1088    283,307    310,350    741,789    870,871

X(86) = isogonal conjugate of X(42)
X(86) = isotomic conjugate of X(10)
X(86) = complement of X(1654)
X(86) = anticomplement of X(1213)
X(86) = X(274)-Ceva conjugate of X(333)
X(86) = cevapoint of X(I) and X(J) for these (I,J): (1,2), (7,77), (21,81)
X(86) = crosssum of X(1) and X(1045)
X(86) = crossdifference of any two points on line X(512)X(798)
X(86) = X(I)-cross conjugate of X(J) for these (I,J): (1,81), (2,274), (7,286), (21,333), (58,27), (513,190)
X(86) = X(I)-beth conjugate of X(J) for these (I,J): (86,1014), (99,86), (261,86), (314,314), (645,86), (811,86)

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