## X(573) (ORTHOHARMONIC OF X(58))

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 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)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.