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) = (cos A)(1 + csc A sin B sin C) + cos B cos C
Trilinears sin(A + π/4)csc2A : sin(B + π/4)csc2B : sin(C + π/4)csc2C (M. Iliev, 4/12/07)
Trilinears (1 + cot A) csc A : (1 + cot B) csc B : (1 + cot C) csc C (M. Iliev, 4/12/07)Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)
Barycentrics b2 + c2 - a2 + 4σ) : c2 + a2 - b2 + 4σ) : a2 + b2 - c2 + 4σ) (M. Iliev, 5/13/07)X(492) is a pole associated with squares that circumscribe ABC. For details and reference, see X(488). (Floor van Lamoen, 4/27/98)
X(492) lies on these lines: 2,6 3,489 4,488 5,638 76,486 315,372 371,641 487,631
X(492) = isotomic conjugate of X(485)
X(492) = anticomplement of X(590)
X(492) = X(264)-Ceva conjugate of X(491)
X(492) = cevapoint of X(2) and X(488)