## X(354) (WEILL POINT)

 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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Download all construction files and macros: tc.zip (10.1 Mb).
This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (b - c)2 - ab - ac : (c - a)2 - bc - ba : (a - b)2 - ca - cb
= 2 + cos B + cos C : 2 + cos C + cos A : 2 + cos A + cos B

Barycentrics    a[(b - c)2 - ab - ac] : b[(c - a)2 - bc - ba] : c[(a - b)2 - ca - cb]

X(354) is the centroid of the intouch triangle.

William Gallatly, The Modern Geometry of the Triangle, 2nd edition, Hodgson, London, 1913, page 16.

X(354) lies on these lines: 1,3    2,210    6,374    7,479    11,118    37,38    42,244    44,748    48,584    63,1001    81,105    278,955    373,375    388,938    392,551    516,553

X(354) = isogonal conjugate of X(2346)
X(354) = inverse-in-incircle of X(1155)
X(354) = reflection of X(I) in X(J) for these (I,J): (210,2), (392,551)
X(354) = X(101)-Ceva conjugate of X(513)
X(354) = crosspoint of X(1) and X(7)
X(354) = crosssum of X(1) and X(55)

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

If you have questions or suggestions, please, contact us using the e-mail presented here.

Departamento de Matemática Aplicada -- Instituto de Matemática -- Universidade Federal Fluminense