X(1153) (CENTER OF THE VAN LAMOEN CIRCLE)

 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           g(a,b,c) : g(b,c,a) : g(c,a,b),
where g(a,b,c) = bc[13a2(b2 + c2) + 10b2c2 - 10a4 - 4b4 - 4c4]

Barycentrics    ag(a,b,c) : bg(b,c,a) : cg(c,a,b)

A triangle is divided by its three medians into 6 smaller triangles. The circumcenters of these smaller triangles are concyclic. Their circle, the Van Lamoen circle, is introduced in

Floor van Lamoen Problem 10830, American Mathematical Monthly 107 (2000) 863; solution by the editors, 109 (2002) 396-397.

Numerous messages about this circle and its center can be accessed from the Hyacinthos archive using "Floor's Monthly problem" as search words. M. Stevanovic's message (#5599, 5/28/02) gives coordinates.

X(1153) lies on these lines: 2,187    140,524    543,549

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