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) = sin A + cot D/2 cos A,
cot D/2 = - (a + b + c)2/(4*area)Trilinears h(a,b,c) : h(b,c,a) : h(c,a,b), where h(a,b,c) = s cos A - r sin A, s = semiperimeter, r = inradius
Barycentrics (sin A)f(A,B,C): (sin B)f(B,C,A) : (sin C)f(C,A,B)
X(573) is the internal center of similitude of the circumcircle and Apollonius circle. The external center is X(386). (Peter J. C. Moses, 8/22/03)
X(573) lies on these lines: 1,941 3,6 4,9 20,391 36,604 37,517 43,165 51,1011 55,181 101,102 109,478 184,199 256,981 346,1018 347,1020
X(573) = reflection of X(991) in X(3)
X(573) = inverse-in-Brocard-circle of X(572)
X(573) = X(333)-Ceva conjugate of X(1)
X(573) = crosspoint of X(59) and X(190)
X(573) = crosssum of X(11) and X(649)
X(573) = crossdifference of any two points on line X(523)X(1459)