## X(185) (NAGEL POINT OF THE 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           (cos A)[1 - cos A cos(B - C)] : (cos B)[1 - cos B cos(C - A)] : (cos C)[1 - cos C cos(A - B)]
Barycentrics    (sin 2A)[1 - cos A cos(B - C)] : (sin 2B)[1 - cos B cos(C - A)] : (sin 2C)[1 - cos C cos(A - B)]

X(185) lies on these lines:
1,296    3,49    4,51    5,113    6,64    20,193    25,1498    30,52    39,217    54,74    72,916    287,384    378,578    382,568    411,970    648,1105

X(185) = reflection of X(I) in X(J) for these (I,J): (4,389), (125,974)
X(185) = isogonal conjugate of X(1105)
X(185) = X(I)-Ceva conjugate of X(J) for these (I,J): (3,417), (4,235)
X(185) = crosspoint of X(3) and X(4)
X(185) = crosssum of X(I) and X(J) for these (I,J): (3,4), (25,1249)

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