## X(1575) (EXSIMILICENTER OF SPIEKER AND (1/2)-MOSES CIRCLES)

 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) = a(b2 + c2) - bc(b + c)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

The Moses circle, M, is introduced at X(1015); the (1/2)-Moses circle is concentric to M with half the radius of M. The insimilicenter of the Spieker and (1/2)-Moses circles is X(1107).

X(1575) lies on these lines:
2,37    6,43    10,39    42,1100    44,513    71,992    172,404    239,292    291,518    519,1015    574,993    1009,1104    1125,1500

X(1575) = complement of X(350)
X(1575) = X(I)-Ceva conjugate of X(J) for these (I,J): (239,518), (292,37)
X(1575) = cevapoint of X(43) and X(2108)
X(1575) = crosspoint of X(2) and X(291)
X(1575) = crosssum of X(I) and X(J) for these (I,J): (1,1575), (6,238)
X(1575) = crossdifference of any two points on line X(1)X(667)

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