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 sec(A/2) csc(A/2 + π/3) : sec(B/2) csc(B/2 + π/3) : sec(C/2) csc(C/2 + π/3)
Barycentrics sin A sec(A/2) csc(A/2 + π/3) : sin B sec(B/2) csc(B/2 + π/3) : sin C sec(C/2) csc(C/2 + π/3)Suppose X and Y are triangle centers. Let
Y_{A} = (Y of the triangle XBC),
Y_{B} = (Y of the triangle XCA),
Y_{C} = (Y of the triangle XAB).Let A' = (XY_{A} intersect BC), and define B' and C' cyclically. In
Clark Kimberling, "Major Centers of Triangles," Amer. Math. Monthly 104 (1997) 431-438,
Question A is this: for what choices of X and Y do the lines AA', BB', CC' concur? A solution (X,Y) will here be called the (X,Y)-answer to Question A. X(554) is the (X(1),X(13))-answer to Question A. (In the reference, see (9) on page 435, with Y = X(13).)