## X(595) (2ND HATZIPOLAKIS-YIU POINT)

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
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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            a(a2 + ab + ac - bc) : b(b2 + bc + ba - ca) : c(c2 + ca + cb - ab)
Barycentrics    a2(a2 + ab + ac - bc) : b2(b2 + bc + ba - ca) : c2(c2 + ca + cb - ab)

Let O(A) be the circle tangent to line BC and to the circumcircle of triangle ABC at vertex A, and define O(B) and O(C) cyclically. X(595) is the radical center of O(A), O(B), O(C).

X(595) lies on these lines: 1,21    3,995    10,82    32,101    35,902    40,602    46,614    55,386    56,106    110,849    171,1125    387,390    517,580

X(595) = isogonal conjugate of X(596)
X(595) = crosssum of X(244) and X(523)

(Antreas Hatzipolakis, Paul Yiu, Hyacinthos #2070)

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