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 -1 + cos B + cos C : -1 + cos C + cos A : -1 + cos A + cos B
Barycentrics (sin A)(-1 + cos B + cos C) : (sin B)(-1 + cos C + cos A) : (sin C)(-1 + cos A + cos B)
As the isogonal conjugate of a point on the circumcircle, X(517) lies on the line at infinity.
X(517) lies on these lines:
1,3 2,392 4,8 5,10 6,998 7,1000 9,374 19,219 20,145 30,511 37,573 42,1064 63,956 78,945 100,953 101,910 104,901 119,908 169,220 210,381 226,495 238,1052 389,950 549,551 572,1100 580,595 582,602 938,1058 1042,1066X(517) = orthopoint of X(513)
X(517) = isogonal conjugate of X(104)
X(517) = anticomplementary conjugate of X(153)
X(517) = complementary conjugate of X(119)
X(517) = X(4)-Ceva conjugate of X(119)
X(517) = crosspoint of X(I) and X(J) for these (I,J): (1,80), (7,88)
X(517) = crosssum of X(I) and X(J) for these (I,J): (1,36), (3,912), (44,55), (56,1455)
X(517) = crossdifference of any two points on line X(6)X(650)