## X(1655) (2ND HATZIPOLAKIS PARALLELIAN POINT)

 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           f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = bc[-1/a2 + 1/b2 + 1/c2 + 1/(bc) + 1/(ca) + 1/(ab)]
Barycentrics    g(a,b,c) : g(b,c,a) : g(c,a,b), where g(a,b,c) = -1/a2 + 1/b2 + 1/c2 + 1/(bc) + 1/(ca) + 1/(ab)

Continuing from the description of X(1654), let h(B,A) be the distance from the point Ba to the line CA, and define five other distances cyclically. If P = X(1655), then

h(B,A) + h(C,A) = h(C,B) + h(A,B) = h(A,C) + h(B,C)

(Antreas Hatzipolakis, Anopolis #20, 1/20/02)

X(1655) lies on these lines: 2,39    8,192    21,385    193,452    350,1107    668,1500

X(1655) = anticomplement of X(274)
X(1655) = X(I)-Ceva conjugate of X(J) for these (I,J): (37,2), (1909,8)

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