## X(1116) (CENTER OF THE LESTER 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           f(a,b,c) : f(b,c,a) : f(c,a,b),
where f(a,b,c) = bc(b2-c2)[2(a2-b2)(c2-a2) + 3R2(2a2-b2-c2) - a2(a2+b2+c2) + a4+b4+c4],
where R = (a csc A)/2 = circumradius of ABC.

Barycentrics    af(a,b,c) : bf(b,c,a): cf(c,a,b)

The Lester circle passes through the points X(3), X(5), X(13), X(14). Coordinates of the center were determined by Milorad Stevanovic (#5895, 9/20/02). The circle is described in

June Lester, "Triangles III: complex centre functions and Ceva's theorem," Aequationes Mathematicae 53 (1997) 4-35.

X(1116) lies on these lines: 115,125    140,523

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