## X(993) (MIDPOINT OF X(1) AND X(63))

 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) = a3 - a(b2 + c2) - bc(b + c)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(993) lies on these lines:
1,21    2,36    3,10    8,35    9,48    32,1107    55,519    56,226    75,99    87,106    238,995    495,529    516,1012    527,551    912,960

X(993) = midpoint of X(I) and X(J) for these (I,J): (1,63), (55,956)
X(993) = reflection of X(226) in X(1125)
X(993) = isogonal conjugate of X(994)
X(993) = complement of X(1478)

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