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 cos A cot A/2 : cos B cot B/2 : cos C cot C/2
= (sin A)/(1 - sec A) : (sin B)/(1 - sec B) : (sin C)/(1 - sec C)
= 1/(csc A - 2 csc 2A) : 1/(csc B - 2 csc 2B) : 1/(csc C - 2 csc 2C)
= a(b + c - a)(b2 + c2 - a2) : b(c + a - b)(c2 + a2 - b2) : c(a + b - c)(a2 + b2 - c2)Barycentrics sin 2A cot A/2 : sin 2B cot B/2 : sin 2C cot C/2
X(219) lies on these lines:
1,6 3,48 8,29 10,965 19,517 40,610 41,1036 55,284 56,579 63,77 101,102 144,347 200,282 206,692 255,268 278,329 332,345 346,644 572,947 577,906 604,672X(219) = isogonal conjugate of X(278)
X(219) = isotomic conjugate of X(331)
X(219) = X(I)-Ceva conjugate of X(J) for these (I,J): (8,55), (63,3), (283,212)
X(219) = X(I)-cross conjugate of X(J) for these (I,J): (48,268), (71,9), (212,3)
X(219) = crosspoint of X(I) and X(J) for these (I,J): (8,345), (64,78)
X(219) = crosssum of X(I) and X(J) for these (I,J): (19,34), (56,608)
X(219) = X(I)-beth conjugate of X(J) for these (I,J): (101,478), (219,48), (644,219)