## X(106) (Λ(INCENTER, 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           a/(2a - b - c) : b/(2b - c - a) : c/(2c - a - b)
Barycentrics    a2/(2a - b - c) : b2/(2b - c - a) : c2/(2c - a - b)

X(106) = Λ(X(1), X(2))
X(106) = Ψ(X(101), X(6))

X(106) lies on these lines:
1,88    2,121    6,101    34,108    36,901    56,109    58,110    86,99    87,932    105,1022    238,898    269,934    292,813    614,998    663,840    789,870    833,977    919,1055

X(106) = reflection of X(1293) in X(3)
X(106) = isogonal conjugate of X(519)
X(106) = anticomplement of X(121)
X(106) = X(36)-cross conjugate of X(58)
X(106) = X(I)-beth conjugate of X(J) for these (I,J): (21,100), (901,106)

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