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 (csc A)/(cot A - cot 2π/5) : (csc B)/(cot B - cot 2π/5) : (csc C)/(cot C - cot 2π/5)
Trilinears csc(A + 3π/5) : csc(B + 3π/5) : csc(C + 3π/5) (Joe Goggins, Oct. 19, 2005)
Barycentrics 1/(cot A - cot 2π/5) : 1/(cot B - cot 2π/5) : 1/(cot C - cot 2π/5)
Let A' be the innermost vertex of the regular pentagon erected inward on side BC of ABC. Define B' and C' cyclically. Then triangle A'B'C' is perspective to ABC, and the perspector is X(1139). See references at X(1139).
X(1140) lies on this line: (6,1139)