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)(1 + cos A) : (cos B)(1 + cos B) : (cos C)(1 + cos C)
= (cos A)cos2(A/2) : (cos B)cos2(B/2) : (cos C)cos2(C/2)
= a2(b + c - a)(b2 + c2 - a2) : b2(c + a - b)(c2 + a2 - b2) : c2(a + b - c)(a2 + b2 - c2)Barycentrics (sin 2A)(1 + cos A) : (sin 2B)(1 + cos B) : (sin 2C)(1 + cos C)
X(212) lies on these lines:
1,201 3,73 6,31 9,33 11,748 34,40 35,47 48,184 56,939 63,1040 78,283 109,165 154,198 238,497 312,643 582,942X(212) = isogonal conjugate of X(273)
X(212) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,48), (9,41), (283,219)
X(212) = X(228)-cross conjugate of X(55)
X(212) = crosspoint of X(I) and X(J) for these (I,J): (3,219), (9,78)
X(212) = crosssum of X(I) and X(J) for these (I,J): (4,278), (34,57)
X(212) = X(212)-beth conjugate of X(184)