## X(1118) (1ST 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 - cos A)/cos2A
Barycentrics    (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)

Let A'B'C' be the intouch triangle of ABC. Let Ca be the point other than C' in which the perpendicular to BC from C' meets the incircle, let Ba be the point other than B' in which the perpendicular to BC from B' meets the incircle, and let A0 be the point of intersection of lines BCa and CBa. Define B0 and C0 cyclically. Then triangle A0B0C0 is perspective to ABC, and the perspector is X(1118). (Antreas Hatzipolakis, #5321, 4/30/02)

X(1118) lies on these lines:
4,65    7,286    12,281    19,208    20,243    24,108    28,56    34,207    92,388

X(1118) = isogonal conjugate of X(1259)
X(1118) = isotomic conjugate of X(1264)

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