## X(1083) (MIDPOINT OF X(105) AND X(644))

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

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) = a4 - a3(b + c) - a2bc + 2abc(b + c) - bc(b2 + c2)
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = af(a,b,c)

X(1083) lies on a circle related to the 1st and 2nd Brocard points; Hyacinthos message #4053, Paul Yiu, Oct. 4, 2001. X(1083) lies on the Brocard circle.

X(1083) lies on these lines:
1,6    3,667    8,1016    55,1026    56,1025    105,644    840,898

X(1083) = midpoint of X(105) and X(644)
X(1083) = inverse-in-circumcircle of X(667)
X(1083) = X(6)-Hirst inverse of X(518)

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