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.
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 105,644 840,898X(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)