## X(1119) (2ND HATZIPOLAKIS PERSPECTOR)

 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) = (1 - sec A)/(1 + cos A)
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Let triangle A0B0C0 be as defined for X(1118). Let A1 be the orthogonal projection of A0 onto line BC, and define B1 and C1 cyclically. Then triangle A1B1C1 is perspective to ABC, and the perspector is X(1119). (Antreas Hatzipolakis, #5321, 4/30/02)

X(1119) lies on these lines:
3,347    4,7    19,57    28,279    34,269    142,281    393,1086    579,1020    915,934

X(1119) = isogonal conjugate of X(1260)
X(1119) = isotomic conjugate of X(1265)
X(1119) = X(34)-cross conjugate of X(278)

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