## X(1279) (MIDPOINT OF X(1) AND X(238))

 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) = (b - c)2 - a(b + c - 2a)
Barycentrics    af(a,b,c) : bf(b,c,a) : cf(c,a,b)

X(1279) lies on these lines:
1,6    31,354    55,614    105,910    145,344    210,748    244,902    513,663    516,1086    551,752    595,942

X(1279) is the {X(1),X(1001)}-harmonic conjugate of X(37).

X(1279) = midpoint of X(1) and X(238)
X(1279) = reflection of X(44) in X(238)
X(1279) = isogonal conjugate of X(1280)
X(1279) = crosspoint of X(I) and X(J) for these (I,J): (1,105), (927,1016)
X(1279) = crosssum of X(I) and X(J) for these (I,J): (1,518), (926,1015)
X(1279) = crossdifference of any two points on line X(9)X(513)

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