## X(53) (SYMMEDIAN POINT OF ORTHIC TRIANGLE)

 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.

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

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           tan A cos(B - C) : tan B cos(C - A) : tan C cos(A - B)
Barycentrics    a tan A cos(B - C) : b tan B cos(C - A) : c tan C cos(A - B)

X(53) lies on these lines:
4,6    5,216    25,157    30,577    45,281    115,133    128,139    137,138    141,264    232,427    273,1086    275,288    311,324    317,524    318,594    395,472    396,473

X(53) is the {X(4),X(393)}-harmonic conjugate of X(6).

X(53) = isogonal conjugate of X(97)
X(53) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,51), (324,5)
X(53) = X(51)-cross conjugate of X(5)
X(53) = crosssum of X(3) and X(577)

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